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575
Distributions.jl
100
function integerunitrange_cdf(d::DiscreteUnivariateDistribution, x::Integer) minimum_d, maximum_d = extrema(d) isfinite(minimum_d) || isfinite(maximum_d) || error("support is unbounded") result = if isfinite(minimum_d) && !(isfinite(maximum_d) && x >= div(minimum_d + maximum_d, 2)) c = sum(Base.Fix...
function integerunitrange_cdf(d::DiscreteUnivariateDistribution, x::Integer) minimum_d, maximum_d = extrema(d) isfinite(minimum_d) || isfinite(maximum_d) || error("support is unbounded") result = if isfinite(minimum_d) && !(isfinite(maximum_d) && x >= div(minimum_d + maximum_d, 2)) c = sum(Base.Fix...
[ 562, 575 ]
function integerunitrange_cdf(d::DiscreteUnivariateDistribution, x::Integer) minimum_d, maximum_d = extrema(d) isfinite(minimum_d) || isfinite(maximum_d) || error("support is unbounded") result = if isfinite(minimum_d) && !(isfinite(maximum_d) && x >= div(minimum_d + maximum_d, 2)) c = sum(Base.Fix...
function integerunitrange_cdf(d::DiscreteUnivariateDistribution, x::Integer) minimum_d, maximum_d = extrema(d) isfinite(minimum_d) || isfinite(maximum_d) || error("support is unbounded") result = if isfinite(minimum_d) && !(isfinite(maximum_d) && x >= div(minimum_d + maximum_d, 2)) c = sum(Base.Fix...
integerunitrange_cdf
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575
src/univariates.jl
#FILE: Distributions.jl/src/truncate.jl ##CHUNK 1 function ccdf(d::Truncated, x::Real) result = clamp((d.ucdf - cdf(d.untruncated, x)) / d.tp, 0, 1) # Special cases for values outside of the support to avoid e.g. NaN issues with `Binomial` return if d.lower !== nothing && x <= d.lower one(result) ...
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Distributions.jl
101
function integerunitrange_ccdf(d::DiscreteUnivariateDistribution, x::Integer) minimum_d, maximum_d = extrema(d) isfinite(minimum_d) || isfinite(maximum_d) || error("support is unbounded") result = if isfinite(minimum_d) && !(isfinite(maximum_d) && x >= div(minimum_d + maximum_d, 2)) c = 1 - sum(Bas...
function integerunitrange_ccdf(d::DiscreteUnivariateDistribution, x::Integer) minimum_d, maximum_d = extrema(d) isfinite(minimum_d) || isfinite(maximum_d) || error("support is unbounded") result = if isfinite(minimum_d) && !(isfinite(maximum_d) && x >= div(minimum_d + maximum_d, 2)) c = 1 - sum(Bas...
[ 577, 590 ]
function integerunitrange_ccdf(d::DiscreteUnivariateDistribution, x::Integer) minimum_d, maximum_d = extrema(d) isfinite(minimum_d) || isfinite(maximum_d) || error("support is unbounded") result = if isfinite(minimum_d) && !(isfinite(maximum_d) && x >= div(minimum_d + maximum_d, 2)) c = 1 - sum(Bas...
function integerunitrange_ccdf(d::DiscreteUnivariateDistribution, x::Integer) minimum_d, maximum_d = extrema(d) isfinite(minimum_d) || isfinite(maximum_d) || error("support is unbounded") result = if isfinite(minimum_d) && !(isfinite(maximum_d) && x >= div(minimum_d + maximum_d, 2)) c = 1 - sum(Bas...
integerunitrange_ccdf
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src/univariates.jl
#FILE: Distributions.jl/src/quantilealgs.jl ##CHUNK 1 return T(minimum(d)) elseif p == 1 return T(maximum(d)) else return T(NaN) end end function cquantile_newton(d::ContinuousUnivariateDistribution, p::Real, xs::Real=mode(d), tol::Real=1e-12) x = xs + (ccdf(d, xs)-p) / pdf(d, x...
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Distributions.jl
102
function integerunitrange_logcdf(d::DiscreteUnivariateDistribution, x::Integer) minimum_d, maximum_d = extrema(d) isfinite(minimum_d) || isfinite(maximum_d) || error("support is unbounded") result = if isfinite(minimum_d) && !(isfinite(maximum_d) && x >= div(minimum_d + maximum_d, 2)) c = logsumexp...
function integerunitrange_logcdf(d::DiscreteUnivariateDistribution, x::Integer) minimum_d, maximum_d = extrema(d) isfinite(minimum_d) || isfinite(maximum_d) || error("support is unbounded") result = if isfinite(minimum_d) && !(isfinite(maximum_d) && x >= div(minimum_d + maximum_d, 2)) c = logsumexp...
[ 592, 605 ]
function integerunitrange_logcdf(d::DiscreteUnivariateDistribution, x::Integer) minimum_d, maximum_d = extrema(d) isfinite(minimum_d) || isfinite(maximum_d) || error("support is unbounded") result = if isfinite(minimum_d) && !(isfinite(maximum_d) && x >= div(minimum_d + maximum_d, 2)) c = logsumexp...
function integerunitrange_logcdf(d::DiscreteUnivariateDistribution, x::Integer) minimum_d, maximum_d = extrema(d) isfinite(minimum_d) || isfinite(maximum_d) || error("support is unbounded") result = if isfinite(minimum_d) && !(isfinite(maximum_d) && x >= div(minimum_d + maximum_d, 2)) c = logsumexp...
integerunitrange_logcdf
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src/univariates.jl
#FILE: Distributions.jl/src/truncate.jl ##CHUNK 1 function ccdf(d::Truncated, x::Real) result = clamp((d.ucdf - cdf(d.untruncated, x)) / d.tp, 0, 1) # Special cases for values outside of the support to avoid e.g. NaN issues with `Binomial` return if d.lower !== nothing && x <= d.lower one(result) ...
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Distributions.jl
103
function integerunitrange_logccdf(d::DiscreteUnivariateDistribution, x::Integer) minimum_d, maximum_d = extrema(d) isfinite(minimum_d) || isfinite(maximum_d) || error("support is unbounded") result = if isfinite(minimum_d) && !(isfinite(maximum_d) && x >= div(minimum_d + maximum_d, 2)) c = log1mexp...
function integerunitrange_logccdf(d::DiscreteUnivariateDistribution, x::Integer) minimum_d, maximum_d = extrema(d) isfinite(minimum_d) || isfinite(maximum_d) || error("support is unbounded") result = if isfinite(minimum_d) && !(isfinite(maximum_d) && x >= div(minimum_d + maximum_d, 2)) c = log1mexp...
[ 607, 620 ]
function integerunitrange_logccdf(d::DiscreteUnivariateDistribution, x::Integer) minimum_d, maximum_d = extrema(d) isfinite(minimum_d) || isfinite(maximum_d) || error("support is unbounded") result = if isfinite(minimum_d) && !(isfinite(maximum_d) && x >= div(minimum_d + maximum_d, 2)) c = log1mexp...
function integerunitrange_logccdf(d::DiscreteUnivariateDistribution, x::Integer) minimum_d, maximum_d = extrema(d) isfinite(minimum_d) || isfinite(maximum_d) || error("support is unbounded") result = if isfinite(minimum_d) && !(isfinite(maximum_d) && x >= div(minimum_d + maximum_d, 2)) c = log1mexp...
integerunitrange_logccdf
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src/univariates.jl
#FILE: Distributions.jl/src/truncate.jl ##CHUNK 1 function ccdf(d::Truncated, x::Real) result = clamp((d.ucdf - cdf(d.untruncated, x)) / d.tp, 0, 1) # Special cases for values outside of the support to avoid e.g. NaN issues with `Binomial` return if d.lower !== nothing && x <= d.lower one(result) ...
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Distributions.jl
104
function LKJCholesky(d::Int, η::Real, _uplo::Union{Char,Symbol} = 'L'; check_args::Bool=true) @check_args( LKJCholesky, (d, d > 0, "matrix dimension must be positive"), (η, η > 0, "shape parameter must be positive"), ) logc0 = lkj_logc0(d, η) uplo = _char_uplo(_uplo) T = Base...
function LKJCholesky(d::Int, η::Real, _uplo::Union{Char,Symbol} = 'L'; check_args::Bool=true) @check_args( LKJCholesky, (d, d > 0, "matrix dimension must be positive"), (η, η > 0, "shape parameter must be positive"), ) logc0 = lkj_logc0(d, η) uplo = _char_uplo(_uplo) T = Base...
[ 43, 53 ]
function LKJCholesky(d::Int, η::Real, _uplo::Union{Char,Symbol} = 'L'; check_args::Bool=true) @check_args( LKJCholesky, (d, d > 0, "matrix dimension must be positive"), (η, η > 0, "shape parameter must be positive"), ) logc0 = lkj_logc0(d, η) uplo = _char_uplo(_uplo) T = Base...
function LKJCholesky(d::Int, η::Real, _uplo::Union{Char,Symbol} = 'L'; check_args::Bool=true) @check_args( LKJCholesky, (d, d > 0, "matrix dimension must be positive"), (η, η > 0, "shape parameter must be positive"), ) logc0 = lkj_logc0(d, η) uplo = _char_uplo(_uplo) T = Base...
LKJCholesky
43
53
src/cholesky/lkjcholesky.jl
#FILE: Distributions.jl/src/matrix/lkj.jl ##CHUNK 1 !!! note if a Cholesky factor of the correlation matrix is desired, it is more efficient to use [`LKJCholesky`](@ref), which avoids factorizing the matrix. """ struct LKJ{T <: Real, D <: Integer} <: ContinuousMatrixDistribution d::D η::T logc0::T e...
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Distributions.jl
105
function insupport(d::LKJCholesky, R::LinearAlgebra.Cholesky) p = d.d factors = R.factors (isreal(factors) && size(factors, 1) == p) || return false iinds, jinds = axes(factors) # check that the diagonal of U'*U or L*L' is all ones @inbounds if R.uplo === 'U' for (j, jind) in enumerate(j...
function insupport(d::LKJCholesky, R::LinearAlgebra.Cholesky) p = d.d factors = R.factors (isreal(factors) && size(factors, 1) == p) || return false iinds, jinds = axes(factors) # check that the diagonal of U'*U or L*L' is all ones @inbounds if R.uplo === 'U' for (j, jind) in enumerate(j...
[ 92, 110 ]
function insupport(d::LKJCholesky, R::LinearAlgebra.Cholesky) p = d.d factors = R.factors (isreal(factors) && size(factors, 1) == p) || return false iinds, jinds = axes(factors) # check that the diagonal of U'*U or L*L' is all ones @inbounds if R.uplo === 'U' for (j, jind) in enumerate(j...
function insupport(d::LKJCholesky, R::LinearAlgebra.Cholesky) p = d.d factors = R.factors (isreal(factors) && size(factors, 1) == p) || return false iinds, jinds = axes(factors) # check that the diagonal of U'*U or L*L' is all ones @inbounds if R.uplo === 'U' for (j, jind) in enumerate(j...
insupport
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src/cholesky/lkjcholesky.jl
#FILE: Distributions.jl/test/cholesky/lkjcholesky.jl ##CHUNK 1 end end end @testset "LKJCholesky marginal KS test" begin α = 0.01 L = sum(1:(p - 1)) for i in 1:p, j in 1:(i-1) @test pvalue_kolmogorovsmirnoff(zs[i, j, :], ma...
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Distributions.jl
106
function logkernel(d::LKJCholesky, R::LinearAlgebra.Cholesky) factors = R.factors p, η = params(d) c = p + 2(η - 1) p == 1 && return c * log(first(factors)) # assuming D = diag(factors) with length(D) = p, # logp = sum(i -> (c - i) * log(D[i]), 2:p) logp = sum(Iterators.drop(enumerate(diagin...
function logkernel(d::LKJCholesky, R::LinearAlgebra.Cholesky) factors = R.factors p, η = params(d) c = p + 2(η - 1) p == 1 && return c * log(first(factors)) # assuming D = diag(factors) with length(D) = p, # logp = sum(i -> (c - i) * log(D[i]), 2:p) logp = sum(Iterators.drop(enumerate(diagin...
[ 130, 141 ]
function logkernel(d::LKJCholesky, R::LinearAlgebra.Cholesky) factors = R.factors p, η = params(d) c = p + 2(η - 1) p == 1 && return c * log(first(factors)) # assuming D = diag(factors) with length(D) = p, # logp = sum(i -> (c - i) * log(D[i]), 2:p) logp = sum(Iterators.drop(enumerate(diagin...
function logkernel(d::LKJCholesky, R::LinearAlgebra.Cholesky) factors = R.factors p, η = params(d) c = p + 2(η - 1) p == 1 && return c * log(first(factors)) # assuming D = diag(factors) with length(D) = p, # logp = sum(i -> (c - i) * log(D[i]), 2:p) logp = sum(Iterators.drop(enumerate(diagin...
logkernel
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src/cholesky/lkjcholesky.jl
#FILE: Distributions.jl/src/matrix/matrixbeta.jl ##CHUNK 1 function logkernel(d::MatrixBeta, U::AbstractMatrix) p, n1, n2 = params(d) ((n1 - p - 1) / 2) * logdet(U) + ((n2 - p - 1) / 2) * logdet(I - U) end # ----------------------------------------------------------------------------- # Sampling # ---------...
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Distributions.jl
107
function Base.rand(rng::AbstractRNG, d::LKJCholesky, dims::Dims) p = d.d uplo = d.uplo T = eltype(d) TM = Matrix{T} Rs = Array{LinearAlgebra.Cholesky{T,TM}}(undef, dims) for i in eachindex(Rs) factors = TM(undef, p, p) Rs[i] = R = LinearAlgebra.Cholesky(factors, uplo, 0) ...
function Base.rand(rng::AbstractRNG, d::LKJCholesky, dims::Dims) p = d.d uplo = d.uplo T = eltype(d) TM = Matrix{T} Rs = Array{LinearAlgebra.Cholesky{T,TM}}(undef, dims) for i in eachindex(Rs) factors = TM(undef, p, p) Rs[i] = R = LinearAlgebra.Cholesky(factors, uplo, 0) ...
[ 166, 178 ]
function Base.rand(rng::AbstractRNG, d::LKJCholesky, dims::Dims) p = d.d uplo = d.uplo T = eltype(d) TM = Matrix{T} Rs = Array{LinearAlgebra.Cholesky{T,TM}}(undef, dims) for i in eachindex(Rs) factors = TM(undef, p, p) Rs[i] = R = LinearAlgebra.Cholesky(factors, uplo, 0) ...
function Base.rand(rng::AbstractRNG, d::LKJCholesky, dims::Dims) p = d.d uplo = d.uplo T = eltype(d) TM = Matrix{T} Rs = Array{LinearAlgebra.Cholesky{T,TM}}(undef, dims) for i in eachindex(Rs) factors = TM(undef, p, p) Rs[i] = R = LinearAlgebra.Cholesky(factors, uplo, 0) ...
Base.rand
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src/cholesky/lkjcholesky.jl
#CURRENT FILE: Distributions.jl/src/cholesky/lkjcholesky.jl ##CHUNK 1 function Random.rand!( rng::AbstractRNG, d::LKJCholesky, Rs::AbstractArray{<:LinearAlgebra.Cholesky{T,TM}}, allocate::Bool, ) where {T,TM} p = d.d uplo = d.uplo if allocate for i in eachindex(Rs) Rs[i]...
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Distributions.jl
108
function Random.rand!( rng::AbstractRNG, d::LKJCholesky, Rs::AbstractArray{<:LinearAlgebra.Cholesky{T,TM}}, allocate::Bool, ) where {T,TM} p = d.d uplo = d.uplo if allocate for i in eachindex(Rs) Rs[i] = _lkj_cholesky_onion_sampler!( rng, d...
function Random.rand!( rng::AbstractRNG, d::LKJCholesky, Rs::AbstractArray{<:LinearAlgebra.Cholesky{T,TM}}, allocate::Bool, ) where {T,TM} p = d.d uplo = d.uplo if allocate for i in eachindex(Rs) Rs[i] = _lkj_cholesky_onion_sampler!( rng, d...
[ 185, 207 ]
function Random.rand!( rng::AbstractRNG, d::LKJCholesky, Rs::AbstractArray{<:LinearAlgebra.Cholesky{T,TM}}, allocate::Bool, ) where {T,TM} p = d.d uplo = d.uplo if allocate for i in eachindex(Rs) Rs[i] = _lkj_cholesky_onion_sampler!( rng, d...
function Random.rand!( rng::AbstractRNG, d::LKJCholesky, Rs::AbstractArray{<:LinearAlgebra.Cholesky{T,TM}}, allocate::Bool, ) where {T,TM} p = d.d uplo = d.uplo if allocate for i in eachindex(Rs) Rs[i] = _lkj_cholesky_onion_sampler!( rng, d...
Random.rand!
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src/cholesky/lkjcholesky.jl
#FILE: Distributions.jl/src/genericrand.jl ##CHUNK 1 end # the function barrier fixes performance issues if `sampler(s)` is type unstable return _rand!(rng, sampler(s), x, allocate) end function _rand!( rng::AbstractRNG, s::Sampleable{ArrayLikeVariate{N}}, x::AbstractArray{<:AbstractArray{<:Rea...
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Distributions.jl
109
function _lkj_cholesky_onion_sampler!( rng::AbstractRNG, d::LKJCholesky, R::LinearAlgebra.Cholesky, ) if R.uplo === 'U' _lkj_cholesky_onion_tri!(rng, R.factors, d.d, d.η, Val(:U)) else _lkj_cholesky_onion_tri!(rng, R.factors, d.d, d.η, Val(:L)) end return R end
function _lkj_cholesky_onion_sampler!( rng::AbstractRNG, d::LKJCholesky, R::LinearAlgebra.Cholesky, ) if R.uplo === 'U' _lkj_cholesky_onion_tri!(rng, R.factors, d.d, d.η, Val(:U)) else _lkj_cholesky_onion_tri!(rng, R.factors, d.d, d.η, Val(:L)) end return R end
[ 221, 232 ]
function _lkj_cholesky_onion_sampler!( rng::AbstractRNG, d::LKJCholesky, R::LinearAlgebra.Cholesky, ) if R.uplo === 'U' _lkj_cholesky_onion_tri!(rng, R.factors, d.d, d.η, Val(:U)) else _lkj_cholesky_onion_tri!(rng, R.factors, d.d, d.η, Val(:L)) end return R end
function _lkj_cholesky_onion_sampler!( rng::AbstractRNG, d::LKJCholesky, R::LinearAlgebra.Cholesky, ) if R.uplo === 'U' _lkj_cholesky_onion_tri!(rng, R.factors, d.d, d.η, Val(:U)) else _lkj_cholesky_onion_tri!(rng, R.factors, d.d, d.η, Val(:L)) end return R end
_lkj_cholesky_onion_sampler!
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src/cholesky/lkjcholesky.jl
#CURRENT FILE: Distributions.jl/src/cholesky/lkjcholesky.jl ##CHUNK 1 function Base.rand(rng::AbstractRNG, d::LKJCholesky) factors = Matrix{eltype(d)}(undef, size(d)) R = LinearAlgebra.Cholesky(factors, d.uplo, 0) return _lkj_cholesky_onion_sampler!(rng, d, R) end function Base.rand(rng::AbstractRNG, d::LKJ...
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Distributions.jl
110
function _lkj_cholesky_onion_tri!( rng::AbstractRNG, A::AbstractMatrix, d::Int, η::Real, ::Val{uplo}, ) where {uplo} # Section 3.2 in LKJ (2009 JMA) # reformulated to incrementally construct Cholesky factor as mentioned in Section 5 # equivalent steps in algorithm in reference are marked...
function _lkj_cholesky_onion_tri!( rng::AbstractRNG, A::AbstractMatrix, d::Int, η::Real, ::Val{uplo}, ) where {uplo} # Section 3.2 in LKJ (2009 JMA) # reformulated to incrementally construct Cholesky factor as mentioned in Section 5 # equivalent steps in algorithm in reference are marked...
[ 234, 272 ]
function _lkj_cholesky_onion_tri!( rng::AbstractRNG, A::AbstractMatrix, d::Int, η::Real, ::Val{uplo}, ) where {uplo} # Section 3.2 in LKJ (2009 JMA) # reformulated to incrementally construct Cholesky factor as mentioned in Section 5 # equivalent steps in algorithm in reference are marked...
function _lkj_cholesky_onion_tri!( rng::AbstractRNG, A::AbstractMatrix, d::Int, η::Real, ::Val{uplo}, ) where {uplo} # Section 3.2 in LKJ (2009 JMA) # reformulated to incrementally construct Cholesky factor as mentioned in Section 5 # equivalent steps in algorithm in reference are marked...
_lkj_cholesky_onion_tri!
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src/cholesky/lkjcholesky.jl
#FILE: Distributions.jl/src/matrix/wishart.jl ##CHUNK 1 fill!(view(A, :, axes2[(r + 1):end]), zero(eltype(A))) else _wishart_genA!(rng, A, d.df) end unwhiten!(d.S, A) A .= A * A' end function _wishart_genA!(rng::AbstractRNG, A::AbstractMatrix, df::Real) # Generate the matrix A in th...
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Distributions.jl
111
function lkj_logc0(d::Integer, η::Real) T = float(Base.promote_typeof(d, η)) d > 1 || return zero(η) if isone(η) if iseven(d) logc0 = -lkj_onion_loginvconst_uniform_even(d, T) else logc0 = -lkj_onion_loginvconst_uniform_odd(d, T) end else logc0 = -...
function lkj_logc0(d::Integer, η::Real) T = float(Base.promote_typeof(d, η)) d > 1 || return zero(η) if isone(η) if iseven(d) logc0 = -lkj_onion_loginvconst_uniform_even(d, T) else logc0 = -lkj_onion_loginvconst_uniform_odd(d, T) end else logc0 = -...
[ 102, 115 ]
function lkj_logc0(d::Integer, η::Real) T = float(Base.promote_typeof(d, η)) d > 1 || return zero(η) if isone(η) if iseven(d) logc0 = -lkj_onion_loginvconst_uniform_even(d, T) else logc0 = -lkj_onion_loginvconst_uniform_odd(d, T) end else logc0 = -...
function lkj_logc0(d::Integer, η::Real) T = float(Base.promote_typeof(d, η)) d > 1 || return zero(η) if isone(η) if iseven(d) logc0 = -lkj_onion_loginvconst_uniform_even(d, T) else logc0 = -lkj_onion_loginvconst_uniform_odd(d, T) end else logc0 = -...
lkj_logc0
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src/matrix/lkj.jl
#FILE: Distributions.jl/test/matrixvariates.jl ##CHUNK 1 end for i in 1:d for j in 1:i-1 @test pvalue_kolmogorovsmirnoff(mymats[i, j, :], ρ) >= α / L end end end @testset "LKJ integrating constant" begin # ============= # odd non-...
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Distributions.jl
112
function _lkj_onion_sampler(d::Integer, η::Real, rng::AbstractRNG = Random.default_rng()) # Section 3.2 in LKJ (2009 JMA) # 1. Initialization R = ones(typeof(η), d, d) d > 1 || return R β = η + 0.5d - 1 u = rand(rng, Beta(β, β)) R[1, 2] = 2u - 1 R[2, 1] = R[1, 2] # 2. for k in...
function _lkj_onion_sampler(d::Integer, η::Real, rng::AbstractRNG = Random.default_rng()) # Section 3.2 in LKJ (2009 JMA) # 1. Initialization R = ones(typeof(η), d, d) d > 1 || return R β = η + 0.5d - 1 u = rand(rng, Beta(β, β)) R[1, 2] = 2u - 1 R[2, 1] = R[1, 2] # 2. for k in...
[ 127, 155 ]
function _lkj_onion_sampler(d::Integer, η::Real, rng::AbstractRNG = Random.default_rng()) # Section 3.2 in LKJ (2009 JMA) # 1. Initialization R = ones(typeof(η), d, d) d > 1 || return R β = η + 0.5d - 1 u = rand(rng, Beta(β, β)) R[1, 2] = 2u - 1 R[2, 1] = R[1, 2] # 2. for k in...
function _lkj_onion_sampler(d::Integer, η::Real, rng::AbstractRNG = Random.default_rng()) # Section 3.2 in LKJ (2009 JMA) # 1. Initialization R = ones(typeof(η), d, d) d > 1 || return R β = η + 0.5d - 1 u = rand(rng, Beta(β, β)) R[1, 2] = 2u - 1 R[2, 1] = R[1, 2] # 2. for k in...
_lkj_onion_sampler
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src/matrix/lkj.jl
#FILE: Distributions.jl/src/cholesky/lkjcholesky.jl ##CHUNK 1 # Section 3.2 in LKJ (2009 JMA) # reformulated to incrementally construct Cholesky factor as mentioned in Section 5 # equivalent steps in algorithm in reference are marked. @assert size(A) == (d, d) A[1, 1] = 1 d > 1 || return A β...
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Distributions.jl
113
function lkj_onion_loginvconst(d::Integer, η::Real) # Equation (17) in LKJ (2009 JMA) T = float(Base.promote_typeof(d, η)) h = T(1//2) α = η + h * d - 1 loginvconst = (2*η + d - 3)*T(logtwo) + (T(logπ) / 4) * (d * (d - 1) - 2) + logbeta(α, α) - (d - 2) * loggamma(η + h * (d - 1)) for k in 2:(d ...
function lkj_onion_loginvconst(d::Integer, η::Real) # Equation (17) in LKJ (2009 JMA) T = float(Base.promote_typeof(d, η)) h = T(1//2) α = η + h * d - 1 loginvconst = (2*η + d - 3)*T(logtwo) + (T(logπ) / 4) * (d * (d - 1) - 2) + logbeta(α, α) - (d - 2) * loggamma(η + h * (d - 1)) for k in 2:(d ...
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function lkj_onion_loginvconst(d::Integer, η::Real) # Equation (17) in LKJ (2009 JMA) T = float(Base.promote_typeof(d, η)) h = T(1//2) α = η + h * d - 1 loginvconst = (2*η + d - 3)*T(logtwo) + (T(logπ) / 4) * (d * (d - 1) - 2) + logbeta(α, α) - (d - 2) * loggamma(η + h * (d - 1)) for k in 2:(d ...
function lkj_onion_loginvconst(d::Integer, η::Real) # Equation (17) in LKJ (2009 JMA) T = float(Base.promote_typeof(d, η)) h = T(1//2) α = η + h * d - 1 loginvconst = (2*η + d - 3)*T(logtwo) + (T(logπ) / 4) * (d * (d - 1) - 2) + logbeta(α, α) - (d - 2) * loggamma(η + h * (d - 1)) for k in 2:(d ...
lkj_onion_loginvconst
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src/matrix/lkj.jl
#CURRENT FILE: Distributions.jl/src/matrix/lkj.jl ##CHUNK 1 function lkj_vine_loginvconst(d::Integer, η::Real) # Equation (16) in LKJ (2009 JMA) expsum = zero(η) betasum = zero(η) for k in 1:d - 1 α = η + 0.5(d - k - 1) expsum += (2η - 2 + d - k) * (d - k) betasum += (d - k) * l...
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function lkj_vine_loginvconst(d::Integer, η::Real) # Equation (16) in LKJ (2009 JMA) expsum = zero(η) betasum = zero(η) for k in 1:d - 1 α = η + 0.5(d - k - 1) expsum += (2η - 2 + d - k) * (d - k) betasum += (d - k) * logbeta(α, α) end loginvconst = expsum * logtwo + bet...
function lkj_vine_loginvconst(d::Integer, η::Real) # Equation (16) in LKJ (2009 JMA) expsum = zero(η) betasum = zero(η) for k in 1:d - 1 α = η + 0.5(d - k - 1) expsum += (2η - 2 + d - k) * (d - k) betasum += (d - k) * logbeta(α, α) end loginvconst = expsum * logtwo + bet...
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function lkj_vine_loginvconst(d::Integer, η::Real) # Equation (16) in LKJ (2009 JMA) expsum = zero(η) betasum = zero(η) for k in 1:d - 1 α = η + 0.5(d - k - 1) expsum += (2η - 2 + d - k) * (d - k) betasum += (d - k) * logbeta(α, α) end loginvconst = expsum * logtwo + bet...
function lkj_vine_loginvconst(d::Integer, η::Real) # Equation (16) in LKJ (2009 JMA) expsum = zero(η) betasum = zero(η) for k in 1:d - 1 α = η + 0.5(d - k - 1) expsum += (2η - 2 + d - k) * (d - k) betasum += (d - k) * logbeta(α, α) end loginvconst = expsum * logtwo + bet...
lkj_vine_loginvconst
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src/matrix/lkj.jl
#FILE: Distributions.jl/test/matrixvariates.jl ##CHUNK 1 end for i in 1:d for j in 1:i-1 @test pvalue_kolmogorovsmirnoff(mymats[i, j, :], ρ) >= α / L end end end @testset "LKJ integrating constant" begin # ============= # odd non-...
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function lkj_vine_loginvconst_uniform(d::Integer) # Equation after (16) in LKJ (2009 JMA) expsum = 0.0 betasum = 0.0 for k in 1:d - 1 α = (k + 1) / 2 expsum += k ^ 2 betasum += k * logbeta(α, α) end loginvconst = expsum * logtwo + betasum return loginvconst end
function lkj_vine_loginvconst_uniform(d::Integer) # Equation after (16) in LKJ (2009 JMA) expsum = 0.0 betasum = 0.0 for k in 1:d - 1 α = (k + 1) / 2 expsum += k ^ 2 betasum += k * logbeta(α, α) end loginvconst = expsum * logtwo + betasum return loginvconst end
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function lkj_vine_loginvconst_uniform(d::Integer) # Equation after (16) in LKJ (2009 JMA) expsum = 0.0 betasum = 0.0 for k in 1:d - 1 α = (k + 1) / 2 expsum += k ^ 2 betasum += k * logbeta(α, α) end loginvconst = expsum * logtwo + betasum return loginvconst end
function lkj_vine_loginvconst_uniform(d::Integer) # Equation after (16) in LKJ (2009 JMA) expsum = 0.0 betasum = 0.0 for k in 1:d - 1 α = (k + 1) / 2 expsum += k ^ 2 betasum += k * logbeta(α, α) end loginvconst = expsum * logtwo + betasum return loginvconst end
lkj_vine_loginvconst_uniform
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src/matrix/lkj.jl
#FILE: Distributions.jl/test/matrixvariates.jl ##CHUNK 1 end for i in 1:d for j in 1:i-1 @test pvalue_kolmogorovsmirnoff(mymats[i, j, :], ρ) >= α / L end end end @testset "LKJ integrating constant" begin # ============= # odd non-...
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Distributions.jl
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function _wishart_genA!(rng::AbstractRNG, A::AbstractMatrix, df::Real) # Generate the matrix A in the Bartlett decomposition # # A is a lower triangular matrix, with # # A(i, j) ~ sqrt of Chisq(df - i + 1) when i == j # ~ Normal() when i > j # T = e...
function _wishart_genA!(rng::AbstractRNG, A::AbstractMatrix, df::Real) # Generate the matrix A in the Bartlett decomposition # # A is a lower triangular matrix, with # # A(i, j) ~ sqrt of Chisq(df - i + 1) when i == j # ~ Normal() when i > j # T = e...
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function _wishart_genA!(rng::AbstractRNG, A::AbstractMatrix, df::Real) # Generate the matrix A in the Bartlett decomposition # # A is a lower triangular matrix, with # # A(i, j) ~ sqrt of Chisq(df - i + 1) when i == j # ~ Normal() when i > j # T = e...
function _wishart_genA!(rng::AbstractRNG, A::AbstractMatrix, df::Real) # Generate the matrix A in the Bartlett decomposition # # A is a lower triangular matrix, with # # A(i, j) ~ sqrt of Chisq(df - i + 1) when i == j # ~ Normal() when i > j # T = e...
_wishart_genA!
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src/matrix/wishart.jl
#FILE: Distributions.jl/src/matrix/inversewishart.jl ##CHUNK 1 (A .= inv(cholesky!(_rand!(rng, Wishart(d.df, inv(d.Ψ)), A)))) # ----------------------------------------------------------------------------- # Test utils # ----------------------------------------------------------------------------- function _un...
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function mean(d::MultivariateMixture) K = ncomponents(d) p = probs(d) m = zeros(length(d)) for i = 1:K pi = p[i] if pi > 0.0 c = component(d, i) axpy!(pi, mean(c), m) end end return m end
function mean(d::MultivariateMixture) K = ncomponents(d) p = probs(d) m = zeros(length(d)) for i = 1:K pi = p[i] if pi > 0.0 c = component(d, i) axpy!(pi, mean(c), m) end end return m end
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function mean(d::MultivariateMixture) K = ncomponents(d) p = probs(d) m = zeros(length(d)) for i = 1:K pi = p[i] if pi > 0.0 c = component(d, i) axpy!(pi, mean(c), m) end end return m end
function mean(d::MultivariateMixture) K = ncomponents(d) p = probs(d) m = zeros(length(d)) for i = 1:K pi = p[i] if pi > 0.0 c = component(d, i) axpy!(pi, mean(c), m) end end return m end
mean
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src/mixtures/mixturemodel.jl
#FILE: Distributions.jl/perf/mixtures.jl ##CHUNK 1 v = 0.0 @inbounds for i in eachindex(p) pi = p[i] if pi > 0.0 c = component(d, i) v += pdf(c, x) * pi end end return v end # compute the overhead of having a mixture function evaluate_manual_pdf(distribut...
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function var(d::UnivariateMixture) K = ncomponents(d) p = probs(d) means = Vector{Float64}(undef, K) m = 0.0 v = 0.0 for i = 1:K pi = p[i] if pi > 0.0 ci = component(d, i) means[i] = mi = mean(ci) m += pi * mi v += pi * var(ci) ...
function var(d::UnivariateMixture) K = ncomponents(d) p = probs(d) means = Vector{Float64}(undef, K) m = 0.0 v = 0.0 for i = 1:K pi = p[i] if pi > 0.0 ci = component(d, i) means[i] = mi = mean(ci) m += pi * mi v += pi * var(ci) ...
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function var(d::UnivariateMixture) K = ncomponents(d) p = probs(d) means = Vector{Float64}(undef, K) m = 0.0 v = 0.0 for i = 1:K pi = p[i] if pi > 0.0 ci = component(d, i) means[i] = mi = mean(ci) m += pi * mi v += pi * var(ci) ...
function var(d::UnivariateMixture) K = ncomponents(d) p = probs(d) means = Vector{Float64}(undef, K) m = 0.0 v = 0.0 for i = 1:K pi = p[i] if pi > 0.0 ci = component(d, i) means[i] = mi = mean(ci) m += pi * mi v += pi * var(ci) ...
var
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src/mixtures/mixturemodel.jl
#FILE: Distributions.jl/perf/mixtures.jl ##CHUNK 1 using BenchmarkTools: @btime import Random using Distributions: AbstractMixtureModel, MixtureModel, LogNormal, Normal, pdf, ncomponents, probs, component, components, ContinuousUnivariateDistribution using Test # v0.22.1 function current_master(d::AbstractMixtureModel...
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function cov(d::MultivariateMixture) K = ncomponents(d) p = probs(d) m = zeros(length(d)) md = zeros(length(d)) V = zeros(length(d),length(d)) for i = 1:K pi = p[i] if pi > 0.0 c = component(d, i) axpy!(pi, mean(c), m) axpy!(pi, cov(c), V) ...
function cov(d::MultivariateMixture) K = ncomponents(d) p = probs(d) m = zeros(length(d)) md = zeros(length(d)) V = zeros(length(d),length(d)) for i = 1:K pi = p[i] if pi > 0.0 c = component(d, i) axpy!(pi, mean(c), m) axpy!(pi, cov(c), V) ...
[ 228, 253 ]
function cov(d::MultivariateMixture) K = ncomponents(d) p = probs(d) m = zeros(length(d)) md = zeros(length(d)) V = zeros(length(d),length(d)) for i = 1:K pi = p[i] if pi > 0.0 c = component(d, i) axpy!(pi, mean(c), m) axpy!(pi, cov(c), V) ...
function cov(d::MultivariateMixture) K = ncomponents(d) p = probs(d) m = zeros(length(d)) md = zeros(length(d)) V = zeros(length(d),length(d)) for i = 1:K pi = p[i] if pi > 0.0 c = component(d, i) axpy!(pi, mean(c), m) axpy!(pi, cov(c), V) ...
cov
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src/mixtures/mixturemodel.jl
#FILE: Distributions.jl/test/mixture.jl ##CHUNK 1 K = ncomponents(g) pr = @inferred(probs(g)) @assert length(pr) == K # mean mu = 0.0 for k = 1:K mu += pr[k] * mean(component(g, k)) end @test @inferred(mean(g)) ≈ mu # evaluation of cdf cf = zeros(T, n) for k = 1:K ...
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function _mixpdf!(r::AbstractArray, d::AbstractMixtureModel, x) K = ncomponents(d) p = probs(d) fill!(r, 0.0) t = Array{eltype(p)}(undef, size(r)) @inbounds for i in eachindex(p) pi = p[i] if pi > 0.0 if d isa UnivariateMixture t .= Base.Fix1(pdf, componen...
function _mixpdf!(r::AbstractArray, d::AbstractMixtureModel, x) K = ncomponents(d) p = probs(d) fill!(r, 0.0) t = Array{eltype(p)}(undef, size(r)) @inbounds for i in eachindex(p) pi = p[i] if pi > 0.0 if d isa UnivariateMixture t .= Base.Fix1(pdf, componen...
[ 293, 310 ]
function _mixpdf!(r::AbstractArray, d::AbstractMixtureModel, x) K = ncomponents(d) p = probs(d) fill!(r, 0.0) t = Array{eltype(p)}(undef, size(r)) @inbounds for i in eachindex(p) pi = p[i] if pi > 0.0 if d isa UnivariateMixture t .= Base.Fix1(pdf, componen...
function _mixpdf!(r::AbstractArray, d::AbstractMixtureModel, x) K = ncomponents(d) p = probs(d) fill!(r, 0.0) t = Array{eltype(p)}(undef, size(r)) @inbounds for i in eachindex(p) pi = p[i] if pi > 0.0 if d isa UnivariateMixture t .= Base.Fix1(pdf, componen...
_mixpdf!
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src/mixtures/mixturemodel.jl
#FILE: Distributions.jl/perf/mixtures.jl ##CHUNK 1 @inbounds c = component(d, i) pdf(c, x) * pi else zero(eltype(p)) end end end function improved_no_inbound(d, x) p = probs(d) return sum(enumerate(p)) do (i, pi) if pi > 0 c = component...
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function _mixlogpdf!(r::AbstractArray, d::AbstractMixtureModel, x) K = ncomponents(d) p = probs(d) n = length(r) Lp = Matrix{eltype(p)}(undef, n, K) m = fill(-Inf, n) @inbounds for i in eachindex(p) pi = p[i] if pi > 0.0 lpri = log(pi) lp_i = view(Lp, :, i...
function _mixlogpdf!(r::AbstractArray, d::AbstractMixtureModel, x) K = ncomponents(d) p = probs(d) n = length(r) Lp = Matrix{eltype(p)}(undef, n, K) m = fill(-Inf, n) @inbounds for i in eachindex(p) pi = p[i] if pi > 0.0 lpri = log(pi) lp_i = view(Lp, :, i...
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function _mixlogpdf!(r::AbstractArray, d::AbstractMixtureModel, x) K = ncomponents(d) p = probs(d) n = length(r) Lp = Matrix{eltype(p)}(undef, n, K) m = fill(-Inf, n) @inbounds for i in eachindex(p) pi = p[i] if pi > 0.0 lpri = log(pi) lp_i = view(Lp, :, i...
function _mixlogpdf!(r::AbstractArray, d::AbstractMixtureModel, x) K = ncomponents(d) p = probs(d) n = length(r) Lp = Matrix{eltype(p)}(undef, n, K) m = fill(-Inf, n) @inbounds for i in eachindex(p) pi = p[i] if pi > 0.0 lpri = log(pi) lp_i = view(Lp, :, i...
_mixlogpdf!
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src/mixtures/mixturemodel.jl
#FILE: Distributions.jl/src/multivariate/jointorderstatistics.jl ##CHUNK 1 issorted(x) && return lp return oftype(lp, -Inf) end i = first(ranks) xᵢ = first(x) if i > 1 # _marginalize_range(d.dist, 0, i, -Inf, xᵢ, T) lp += (i - 1) * logcdf(d.dist, xᵢ) - loggamma(T(i)) end ...
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function cov(d::Dirichlet) α = d.alpha α0 = d.alpha0 c = inv(α0^2 * (α0 + 1)) T = typeof(zero(eltype(α))^2 * c) k = length(α) C = Matrix{T}(undef, k, k) for j = 1:k αj = α[j] αjc = αj * c for i in 1:(j-1) @inbounds C[i,j] = C[j,i] end @inb...
function cov(d::Dirichlet) α = d.alpha α0 = d.alpha0 c = inv(α0^2 * (α0 + 1)) T = typeof(zero(eltype(α))^2 * c) k = length(α) C = Matrix{T}(undef, k, k) for j = 1:k αj = α[j] αjc = αj * c for i in 1:(j-1) @inbounds C[i,j] = C[j,i] end @inb...
[ 86, 107 ]
function cov(d::Dirichlet) α = d.alpha α0 = d.alpha0 c = inv(α0^2 * (α0 + 1)) T = typeof(zero(eltype(α))^2 * c) k = length(α) C = Matrix{T}(undef, k, k) for j = 1:k αj = α[j] αjc = αj * c for i in 1:(j-1) @inbounds C[i,j] = C[j,i] end @inb...
function cov(d::Dirichlet) α = d.alpha α0 = d.alpha0 c = inv(α0^2 * (α0 + 1)) T = typeof(zero(eltype(α))^2 * c) k = length(α) C = Matrix{T}(undef, k, k) for j = 1:k αj = α[j] αjc = αj * c for i in 1:(j-1) @inbounds C[i,j] = C[j,i] end @inb...
cov
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src/multivariate/dirichlet.jl
#FILE: Distributions.jl/src/multivariate/dirichletmultinomial.jl ##CHUNK 1 function var(d::DirichletMultinomial{T}) where T <: Real v = fill(d.n * (d.n + d.α0) / (1 + d.α0), length(d)) p = d.α / d.α0 for i in eachindex(v) @inbounds v[i] *= p[i] * (1 - p[i]) end v end function cov(d::Dirichle...
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function JointOrderStatistics( dist::ContinuousUnivariateDistribution, n::Int, ranks::Union{AbstractVector{Int},Tuple{Int,Vararg{Int}}}=Base.OneTo(n); check_args::Bool=true, ) @check_args( JointOrderStatistics, (n, n ≥ 1, "`n` must be a positive intege...
function JointOrderStatistics( dist::ContinuousUnivariateDistribution, n::Int, ranks::Union{AbstractVector{Int},Tuple{Int,Vararg{Int}}}=Base.OneTo(n); check_args::Bool=true, ) @check_args( JointOrderStatistics, (n, n ≥ 1, "`n` must be a positive intege...
[ 43, 59 ]
function JointOrderStatistics( dist::ContinuousUnivariateDistribution, n::Int, ranks::Union{AbstractVector{Int},Tuple{Int,Vararg{Int}}}=Base.OneTo(n); check_args::Bool=true, ) @check_args( JointOrderStatistics, (n, n ≥ 1, "`n` must be a positive intege...
function JointOrderStatistics( dist::ContinuousUnivariateDistribution, n::Int, ranks::Union{AbstractVector{Int},Tuple{Int,Vararg{Int}}}=Base.OneTo(n); check_args::Bool=true, ) @check_args( JointOrderStatistics, (n, n ≥ 1, "`n` must be a positive intege...
JointOrderStatistics
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src/multivariate/jointorderstatistics.jl
#FILE: Distributions.jl/src/univariate/orderstatistic.jl ##CHUNK 1 For the joint distribution of a subset of order statistics, use [`JointOrderStatistics`](@ref) instead. ## Examples ```julia OrderStatistic(Cauchy(), 10, 1) # distribution of the sample minimum OrderStatistic(DiscreteUniform(10), 10, 10) ...
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function insupport(d::JointOrderStatistics, x::AbstractVector) length(d) == length(x) || return false xi, state = iterate(x) # at least one element! dist = d.dist insupport(dist, xi) || return false while (xj_state = iterate(x, state)) !== nothing xj, state = xj_state xj ≥ xi && insu...
function insupport(d::JointOrderStatistics, x::AbstractVector) length(d) == length(x) || return false xi, state = iterate(x) # at least one element! dist = d.dist insupport(dist, xi) || return false while (xj_state = iterate(x, state)) !== nothing xj, state = xj_state xj ≥ xi && insu...
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function insupport(d::JointOrderStatistics, x::AbstractVector) length(d) == length(x) || return false xi, state = iterate(x) # at least one element! dist = d.dist insupport(dist, xi) || return false while (xj_state = iterate(x, state)) !== nothing xj, state = xj_state xj ≥ xi && insu...
function insupport(d::JointOrderStatistics, x::AbstractVector) length(d) == length(x) || return false xi, state = iterate(x) # at least one element! dist = d.dist insupport(dist, xi) || return false while (xj_state = iterate(x, state)) !== nothing xj, state = xj_state xj ≥ xi && insu...
insupport
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src/multivariate/jointorderstatistics.jl
#FILE: Distributions.jl/src/univariates.jl ##CHUNK 1 """ insupport(d::UnivariateDistribution, x::Any) When `x` is a scalar, it returns whether x is within the support of `d` (e.g., `insupport(d, x) = minimum(d) <= x <= maximum(d)`). When `x` is an array, it returns whether every element in x is within the support...
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function logpdf(d::JointOrderStatistics, x::AbstractVector{<:Real}) n = d.n ranks = d.ranks lp = loglikelihood(d.dist, x) T = typeof(lp) lp += loggamma(T(n + 1)) if length(ranks) == n issorted(x) && return lp return oftype(lp, -Inf) end i = first(ranks) xᵢ = first(x) ...
function logpdf(d::JointOrderStatistics, x::AbstractVector{<:Real}) n = d.n ranks = d.ranks lp = loglikelihood(d.dist, x) T = typeof(lp) lp += loggamma(T(n + 1)) if length(ranks) == n issorted(x) && return lp return oftype(lp, -Inf) end i = first(ranks) xᵢ = first(x) ...
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function logpdf(d::JointOrderStatistics, x::AbstractVector{<:Real}) n = d.n ranks = d.ranks lp = loglikelihood(d.dist, x) T = typeof(lp) lp += loggamma(T(n + 1)) if length(ranks) == n issorted(x) && return lp return oftype(lp, -Inf) end i = first(ranks) xᵢ = first(x) ...
function logpdf(d::JointOrderStatistics, x::AbstractVector{<:Real}) n = d.n ranks = d.ranks lp = loglikelihood(d.dist, x) T = typeof(lp) lp += loggamma(T(n + 1)) if length(ranks) == n issorted(x) && return lp return oftype(lp, -Inf) end i = first(ranks) xᵢ = first(x) ...
logpdf
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src/multivariate/jointorderstatistics.jl
#FILE: Distributions.jl/test/multivariate/jointorderstatistics.jl ##CHUNK 1 @test !insupport(d, fill(NaN, length(x))) end @testset "pdf/logpdf" begin x = convert(Vector{T}, sort(rand(dist, length(r)))) @test @inferred(logpdf(d, x)) isa T @test @inferred(p...
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function _rand!(rng::AbstractRNG, d::JointOrderStatistics, x::AbstractVector{<:Real}) n = d.n if n == length(d.ranks) # ranks == 1:n # direct method, slower than inversion method for large `n` and distributions with # fast quantile function or that use inversion sampling rand!(rng, d.di...
function _rand!(rng::AbstractRNG, d::JointOrderStatistics, x::AbstractVector{<:Real}) n = d.n if n == length(d.ranks) # ranks == 1:n # direct method, slower than inversion method for large `n` and distributions with # fast quantile function or that use inversion sampling rand!(rng, d.di...
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function _rand!(rng::AbstractRNG, d::JointOrderStatistics, x::AbstractVector{<:Real}) n = d.n if n == length(d.ranks) # ranks == 1:n # direct method, slower than inversion method for large `n` and distributions with # fast quantile function or that use inversion sampling rand!(rng, d.di...
function _rand!(rng::AbstractRNG, d::JointOrderStatistics, x::AbstractVector{<:Real}) n = d.n if n == length(d.ranks) # ranks == 1:n # direct method, slower than inversion method for large `n` and distributions with # fast quantile function or that use inversion sampling rand!(rng, d.di...
_rand!
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src/multivariate/jointorderstatistics.jl
#FILE: Distributions.jl/src/univariate/continuous/pgeneralizedgaussian.jl ##CHUNK 1 return log1pexp(logcdf(d, r)) - logtwo end end function quantile(d::PGeneralizedGaussian, q::Real) μ, α, p = params(d) inv_p = inv(p) r = 2 * q - 1 z = α * quantile(Gamma(inv_p, 1), abs(r))^inv_p return ...
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function entropy(d::Multinomial) n, p = params(d) s = -loggamma(n+1) + n*entropy(p) for pr in p b = Binomial(n, pr) for x in 0:n s += pdf(b, x) * loggamma(x+1) end end return s end
function entropy(d::Multinomial) n, p = params(d) s = -loggamma(n+1) + n*entropy(p) for pr in p b = Binomial(n, pr) for x in 0:n s += pdf(b, x) * loggamma(x+1) end end return s end
[ 120, 130 ]
function entropy(d::Multinomial) n, p = params(d) s = -loggamma(n+1) + n*entropy(p) for pr in p b = Binomial(n, pr) for x in 0:n s += pdf(b, x) * loggamma(x+1) end end return s end
function entropy(d::Multinomial) n, p = params(d) s = -loggamma(n+1) + n*entropy(p) for pr in p b = Binomial(n, pr) for x in 0:n s += pdf(b, x) * loggamma(x+1) end end return s end
entropy
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src/multivariate/multinomial.jl
#FILE: Distributions.jl/src/univariate/discrete/binomial.jl ##CHUNK 1 end function kurtosis(d::Binomial) n, p = params(d) u = p * (1 - p) (1 - 6u) / (n * u) end function entropy(d::Binomial; approx::Bool=false) n, p1 = params(d) (p1 == 0 || p1 == 1 || n == 0) && return zero(p1) p0 = 1 - p1 ...
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Distributions.jl
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function insupport(d::Multinomial, x::AbstractVector{T}) where T<:Real k = length(d) length(x) == k || return false s = 0.0 for i = 1:k @inbounds xi = x[i] if !(isinteger(xi) && xi >= 0) return false end s += xi end return s == ntrials(d) # integer co...
function insupport(d::Multinomial, x::AbstractVector{T}) where T<:Real k = length(d) length(x) == k || return false s = 0.0 for i = 1:k @inbounds xi = x[i] if !(isinteger(xi) && xi >= 0) return false end s += xi end return s == ntrials(d) # integer co...
[ 135, 147 ]
function insupport(d::Multinomial, x::AbstractVector{T}) where T<:Real k = length(d) length(x) == k || return false s = 0.0 for i = 1:k @inbounds xi = x[i] if !(isinteger(xi) && xi >= 0) return false end s += xi end return s == ntrials(d) # integer co...
function insupport(d::Multinomial, x::AbstractVector{T}) where T<:Real k = length(d) length(x) == k || return false s = 0.0 for i = 1:k @inbounds xi = x[i] if !(isinteger(xi) && xi >= 0) return false end s += xi end return s == ntrials(d) # integer co...
insupport
135
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src/multivariate/multinomial.jl
#FILE: Distributions.jl/src/univariate/discrete/discretenonparametric.jl ##CHUNK 1 # trivial cases x < minimum(d) && return one(P) x >= maximum(d) && return zero(P) isnan(x) && return P(NaN) n = length(ps) stop_idx = searchsortedlast(support(d), x) s = zero(P) if stop_idx < div(n, 2) ...
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Distributions.jl
129
function _logpdf(d::Multinomial, x::AbstractVector{T}) where T<:Real p = probs(d) n = ntrials(d) S = eltype(p) R = promote_type(T, S) insupport(d,x) || return -R(Inf) s = R(loggamma(n + 1)) for i = 1:length(p) @inbounds xi = x[i] @inbounds p_i = p[i] s -= R(loggamma(R...
function _logpdf(d::Multinomial, x::AbstractVector{T}) where T<:Real p = probs(d) n = ntrials(d) S = eltype(p) R = promote_type(T, S) insupport(d,x) || return -R(Inf) s = R(loggamma(n + 1)) for i = 1:length(p) @inbounds xi = x[i] @inbounds p_i = p[i] s -= R(loggamma(R...
[ 149, 163 ]
function _logpdf(d::Multinomial, x::AbstractVector{T}) where T<:Real p = probs(d) n = ntrials(d) S = eltype(p) R = promote_type(T, S) insupport(d,x) || return -R(Inf) s = R(loggamma(n + 1)) for i = 1:length(p) @inbounds xi = x[i] @inbounds p_i = p[i] s -= R(loggamma(R...
function _logpdf(d::Multinomial, x::AbstractVector{T}) where T<:Real p = probs(d) n = ntrials(d) S = eltype(p) R = promote_type(T, S) insupport(d,x) || return -R(Inf) s = R(loggamma(n + 1)) for i = 1:length(p) @inbounds xi = x[i] @inbounds p_i = p[i] s -= R(loggamma(R...
_logpdf
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src/multivariate/multinomial.jl
#FILE: Distributions.jl/src/mixtures/mixturemodel.jl ##CHUNK 1 function _mixlogpdf1(d::AbstractMixtureModel, x) p = probs(d) lp = logsumexp(log(pi) + logpdf(component(d, i), x) for (i, pi) in enumerate(p) if !iszero(pi)) return lp end function _mixlogpdf!(r::AbstractArray, d::AbstractMixtureModel, x) ...
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Distributions.jl
130
function _vmf_estkappa(p::Int, ρ::Float64) # Using the fixed-point iteration algorithm in the following paper: # # Akihiro Tanabe, Kenji Fukumizu, and Shigeyuki Oba, Takashi Takenouchi, and Shin Ishii # Parameter estimation for von Mises-Fisher distributions. # Computational Statistics, 2007, ...
function _vmf_estkappa(p::Int, ρ::Float64) # Using the fixed-point iteration algorithm in the following paper: # # Akihiro Tanabe, Kenji Fukumizu, and Shigeyuki Oba, Takashi Takenouchi, and Shin Ishii # Parameter estimation for von Mises-Fisher distributions. # Computational Statistics, 2007, ...
[ 100, 125 ]
function _vmf_estkappa(p::Int, ρ::Float64) # Using the fixed-point iteration algorithm in the following paper: # # Akihiro Tanabe, Kenji Fukumizu, and Shigeyuki Oba, Takashi Takenouchi, and Shin Ishii # Parameter estimation for von Mises-Fisher distributions. # Computational Statistics, 2007, ...
function _vmf_estkappa(p::Int, ρ::Float64) # Using the fixed-point iteration algorithm in the following paper: # # Akihiro Tanabe, Kenji Fukumizu, and Shigeyuki Oba, Takashi Takenouchi, and Shin Ishii # Parameter estimation for von Mises-Fisher distributions. # Computational Statistics, 2007, ...
_vmf_estkappa
100
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src/multivariate/vonmisesfisher.jl
#FILE: Distributions.jl/src/samplers/vonmises.jl ##CHUNK 1 struct VonMisesSampler <: Sampleable{Univariate,Continuous} μ::Float64 κ::Float64 r::Float64 function VonMisesSampler(μ::Float64, κ::Float64) τ = 1.0 + sqrt(1.0 + 4 * abs2(κ)) ρ = (τ - sqrt(2.0 * τ)) / (2.0 * κ) new(μ, ...
3
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Distributions.jl
131
function binompvec(n::Int, p::Float64) pv = Vector{Float64}(undef, n+1) if p == 0.0 fill!(pv, 0.0) pv[1] = 1.0 elseif p == 1.0 fill!(pv, 0.0) pv[n+1] = 1.0 else q = 1.0 - p a = p / q @inbounds pv[1] = pk = q ^ n for k = 1:n @inb...
function binompvec(n::Int, p::Float64) pv = Vector{Float64}(undef, n+1) if p == 0.0 fill!(pv, 0.0) pv[1] = 1.0 elseif p == 1.0 fill!(pv, 0.0) pv[n+1] = 1.0 else q = 1.0 - p a = p / q @inbounds pv[1] = pk = q ^ n for k = 1:n @inb...
[ 3, 20 ]
function binompvec(n::Int, p::Float64) pv = Vector{Float64}(undef, n+1) if p == 0.0 fill!(pv, 0.0) pv[1] = 1.0 elseif p == 1.0 fill!(pv, 0.0) pv[n+1] = 1.0 else q = 1.0 - p a = p / q @inbounds pv[1] = pk = q ^ n for k = 1:n @inb...
function binompvec(n::Int, p::Float64) pv = Vector{Float64}(undef, n+1) if p == 0.0 fill!(pv, 0.0) pv[1] = 1.0 elseif p == 1.0 fill!(pv, 0.0) pv[n+1] = 1.0 else q = 1.0 - p a = p / q @inbounds pv[1] = pk = q ^ n for k = 1:n @inb...
binompvec
3
20
src/samplers/binomial.jl
#FILE: Distributions.jl/src/univariate/discrete/poissonbinomial.jl ##CHUNK 1 kp1 = k + 1 for j in 1:(i - 1) A[j, k] = pi * A[j, k] + qi * A[j, kp1] end for j in (i+1):n A[j, k] = pi * A[j, k] + qi * A[j, kp1] end end ...
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Distributions.jl
132
function rand(rng::AbstractRNG, s::CategoricalDirectSampler) p = s.prob n = length(p) i = 1 c = p[1] u = rand(rng) while c < u && i < n c += p[i += 1] end return i end
function rand(rng::AbstractRNG, s::CategoricalDirectSampler) p = s.prob n = length(p) i = 1 c = p[1] u = rand(rng) while c < u && i < n c += p[i += 1] end return i end
[ 18, 28 ]
function rand(rng::AbstractRNG, s::CategoricalDirectSampler) p = s.prob n = length(p) i = 1 c = p[1] u = rand(rng) while c < u && i < n c += p[i += 1] end return i end
function rand(rng::AbstractRNG, s::CategoricalDirectSampler) p = s.prob n = length(p) i = 1 c = p[1] u = rand(rng) while c < u && i < n c += p[i += 1] end return i end
rand
18
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src/samplers/categorical.jl
#FILE: Distributions.jl/src/univariate/discrete/discretenonparametric.jl ##CHUNK 1 isapprox(probs(c1), probs(c2); kwargs...) end # Sampling function rand(rng::AbstractRNG, d::DiscreteNonParametric) x = support(d) p = probs(d) n = length(p) draw = rand(rng, float(eltype(p))) cp = p[1] i...
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Distributions.jl
133
function rand(rng::AbstractRNG, s::GammaGDSampler) # Step 2 t = randn(rng) x = s.s + 0.5t t >= 0.0 && return x*x*s.scale # Step 3 u = rand(rng) s.d*u <= t*t*t && return x*x*s.scale # Step 5 if x > 0.0 # Step 6 q = calc_q(s, t) # Step 7 log1p(-u) <= q...
function rand(rng::AbstractRNG, s::GammaGDSampler) # Step 2 t = randn(rng) x = s.s + 0.5t t >= 0.0 && return x*x*s.scale # Step 3 u = rand(rng) s.d*u <= t*t*t && return x*x*s.scale # Step 5 if x > 0.0 # Step 6 q = calc_q(s, t) # Step 7 log1p(-u) <= q...
[ 78, 119 ]
function rand(rng::AbstractRNG, s::GammaGDSampler) # Step 2 t = randn(rng) x = s.s + 0.5t t >= 0.0 && return x*x*s.scale # Step 3 u = rand(rng) s.d*u <= t*t*t && return x*x*s.scale # Step 5 if x > 0.0 # Step 6 q = calc_q(s, t) # Step 7 log1p(-u) <= q...
function rand(rng::AbstractRNG, s::GammaGDSampler) # Step 2 t = randn(rng) x = s.s + 0.5t t >= 0.0 && return x*x*s.scale # Step 3 u = rand(rng) s.d*u <= t*t*t && return x*x*s.scale # Step 5 if x > 0.0 # Step 6 q = calc_q(s, t) # Step 7 log1p(-u) <= q...
rand
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src/samplers/gamma.jl
#FILE: Distributions.jl/src/samplers/vonmises.jl ##CHUNK 1 u = 4 * (d + e) break end end z = (1.0 - t) / (1.0 + t) f = (1.0 + s.r * z) / (s.r + z) c = s.κ * (s.r - f) if c * (2.0 - c) > u || log(c / u) + ...
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Distributions.jl
134
function GammaMTSampler(g::Gamma) # Setup (Step 1) d = shape(g) - 1//3 c = inv(3 * sqrt(d)) # Pre-compute scaling factor κ = d * scale(g) # We also pre-compute the factor in the squeeze function return GammaMTSampler(promote(d, c, κ, 331//10_000)...) end
function GammaMTSampler(g::Gamma) # Setup (Step 1) d = shape(g) - 1//3 c = inv(3 * sqrt(d)) # Pre-compute scaling factor κ = d * scale(g) # We also pre-compute the factor in the squeeze function return GammaMTSampler(promote(d, c, κ, 331//10_000)...) end
[ 173, 183 ]
function GammaMTSampler(g::Gamma) # Setup (Step 1) d = shape(g) - 1//3 c = inv(3 * sqrt(d)) # Pre-compute scaling factor κ = d * scale(g) # We also pre-compute the factor in the squeeze function return GammaMTSampler(promote(d, c, κ, 331//10_000)...) end
function GammaMTSampler(g::Gamma) # Setup (Step 1) d = shape(g) - 1//3 c = inv(3 * sqrt(d)) # Pre-compute scaling factor κ = d * scale(g) # We also pre-compute the factor in the squeeze function return GammaMTSampler(promote(d, c, κ, 331//10_000)...) end
GammaMTSampler
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183
src/samplers/gamma.jl
#FILE: Distributions.jl/src/univariate/continuous/gamma.jl ##CHUNK 1 insupport(Gamma, x) ? (d.α - 1) / x - 1 / d.θ : zero(T) function rand(rng::AbstractRNG, d::Gamma) if shape(d) < 1.0 # TODO: shape(d) = 0.5 : use scaled chisq return rand(rng, GammaIPSampler(d)) elseif shape(d) == 1.0 ...
1
40
Distributions.jl
135
function multinom_rand!(rng::AbstractRNG, n::Int, p::AbstractVector{<:Real}, x::AbstractVector{<:Real}) k = length(p) length(x) == k || throw(DimensionMismatch("Invalid argument dimension.")) z = zero(eltype(p)) rp = oftype(z + z, 1) # remaining total probability (widens type i...
function multinom_rand!(rng::AbstractRNG, n::Int, p::AbstractVector{<:Real}, x::AbstractVector{<:Real}) k = length(p) length(x) == k || throw(DimensionMismatch("Invalid argument dimension.")) z = zero(eltype(p)) rp = oftype(z + z, 1) # remaining total probability (widens type i...
[ 1, 40 ]
function multinom_rand!(rng::AbstractRNG, n::Int, p::AbstractVector{<:Real}, x::AbstractVector{<:Real}) k = length(p) length(x) == k || throw(DimensionMismatch("Invalid argument dimension.")) z = zero(eltype(p)) rp = oftype(z + z, 1) # remaining total probability (widens type i...
function multinom_rand!(rng::AbstractRNG, n::Int, p::AbstractVector{<:Real}, x::AbstractVector{<:Real}) k = length(p) length(x) == k || throw(DimensionMismatch("Invalid argument dimension.")) z = zero(eltype(p)) rp = oftype(z + z, 1) # remaining total probability (widens type i...
multinom_rand!
1
40
src/samplers/multinomial.jl
#FILE: Distributions.jl/src/univariate/discrete/binomial.jl ##CHUNK 1 z = zero(eltype(x)) ns = z + z # possibly widened and different from `z`, e.g., if `z = true` for xi in x 0 <= xi <= n || throw(DomainError(xi, "samples must be between 0 and $n")) ns += xi end BinomialStats(ns, le...
52
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Distributions.jl
136
function _rand!(rng::AbstractRNG, s::MultinomialSampler, x::AbstractVector{<:Real}) n = s.n k = length(s) if n^2 > k multinom_rand!(rng, n, s.prob, x) else # Use an alias table fill!(x, zero(eltype(x))) a = s.alias for i = 1:n x[rand(rn...
function _rand!(rng::AbstractRNG, s::MultinomialSampler, x::AbstractVector{<:Real}) n = s.n k = length(s) if n^2 > k multinom_rand!(rng, n, s.prob, x) else # Use an alias table fill!(x, zero(eltype(x))) a = s.alias for i = 1:n x[rand(rn...
[ 52, 67 ]
function _rand!(rng::AbstractRNG, s::MultinomialSampler, x::AbstractVector{<:Real}) n = s.n k = length(s) if n^2 > k multinom_rand!(rng, n, s.prob, x) else # Use an alias table fill!(x, zero(eltype(x))) a = s.alias for i = 1:n x[rand(rn...
function _rand!(rng::AbstractRNG, s::MultinomialSampler, x::AbstractVector{<:Real}) n = s.n k = length(s) if n^2 > k multinom_rand!(rng, n, s.prob, x) else # Use an alias table fill!(x, zero(eltype(x))) a = s.alias for i = 1:n x[rand(rn...
_rand!
52
67
src/samplers/multinomial.jl
#FILE: Distributions.jl/src/multivariate/multinomial.jl ##CHUNK 1 n = ntrials(d) S = eltype(p) R = promote_type(T, S) insupport(d,x) || return -R(Inf) s = R(loggamma(n + 1)) for i = 1:length(p) @inbounds xi = x[i] @inbounds p_i = p[i] s -= R(loggamma(R(xi) + 1)) s...
16
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Distributions.jl
137
function DiscreteDistributionTable(probs::Vector{T}) where T <: Real # Cache the cardinality of the outcome set n = length(probs) # Convert all Float64's into integers vals = Vector{Int64}(undef, n) for i in 1:n vals[i] = round(Int, probs[i] * 64^9) end # Allocate digit table and d...
function DiscreteDistributionTable(probs::Vector{T}) where T <: Real # Cache the cardinality of the outcome set n = length(probs) # Convert all Float64's into integers vals = Vector{Int64}(undef, n) for i in 1:n vals[i] = round(Int, probs[i] * 64^9) end # Allocate digit table and d...
[ 16, 69 ]
function DiscreteDistributionTable(probs::Vector{T}) where T <: Real # Cache the cardinality of the outcome set n = length(probs) # Convert all Float64's into integers vals = Vector{Int64}(undef, n) for i in 1:n vals[i] = round(Int, probs[i] * 64^9) end # Allocate digit table and d...
function DiscreteDistributionTable(probs::Vector{T}) where T <: Real # Cache the cardinality of the outcome set n = length(probs) # Convert all Float64's into integers vals = Vector{Int64}(undef, n) for i in 1:n vals[i] = round(Int, probs[i] * 64^9) end # Allocate digit table and d...
DiscreteDistributionTable
16
69
src/samplers/obsoleted.jl
#FILE: Distributions.jl/src/multivariate/multinomial.jl ##CHUNK 1 MultinomialStats(n::Int, scnts::Vector{Float64}, tw::Real) = new(n, scnts, Float64(tw)) end function suffstats(::Type{<:Multinomial}, x::Matrix{T}) where T<:Real K = size(x, 1) n::T = zero(T) scnts = zeros(K) for j = 1:size(x,2) ...
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Distributions.jl
138
function rand(table::DiscreteDistributionTable) # 64^9 - 1 == 0x003fffffffffffff i = rand(1:(64^9 - 1)) # if i == 64^9 # return table.table[9][rand(1:length(table.table[9]))] # end bound = 1 while i > table.bounds[bound] && bound < 9 bound += 1 end if bound > 1 inde...
function rand(table::DiscreteDistributionTable) # 64^9 - 1 == 0x003fffffffffffff i = rand(1:(64^9 - 1)) # if i == 64^9 # return table.table[9][rand(1:length(table.table[9]))] # end bound = 1 while i > table.bounds[bound] && bound < 9 bound += 1 end if bound > 1 inde...
[ 71, 87 ]
function rand(table::DiscreteDistributionTable) # 64^9 - 1 == 0x003fffffffffffff i = rand(1:(64^9 - 1)) # if i == 64^9 # return table.table[9][rand(1:length(table.table[9]))] # end bound = 1 while i > table.bounds[bound] && bound < 9 bound += 1 end if bound > 1 inde...
function rand(table::DiscreteDistributionTable) # 64^9 - 1 == 0x003fffffffffffff i = rand(1:(64^9 - 1)) # if i == 64^9 # return table.table[9][rand(1:length(table.table[9]))] # end bound = 1 while i > table.bounds[bound] && bound < 9 bound += 1 end if bound > 1 inde...
rand
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87
src/samplers/obsoleted.jl
#FILE: Distributions.jl/test/truncated/discrete_uniform.jl ##CHUNK 1 using Distributions, Test @testset "truncated DiscreteUniform" begin # just test equivalence of truncation results bounds = [(1, 10), (-3, 7), (-5, -2)] @testset "lower=$lower, upper=$upper" for (lower, upper) in bounds d = Discre...
22
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Distributions.jl
139
function rand(rng::AbstractRNG, s::PoissonCountSampler) μ = s.μ T = typeof(μ) n = 0 c = randexp(rng, T) while c < μ n += 1 c += randexp(rng, T) end return n end
function rand(rng::AbstractRNG, s::PoissonCountSampler) μ = s.μ T = typeof(μ) n = 0 c = randexp(rng, T) while c < μ n += 1 c += randexp(rng, T) end return n end
[ 22, 32 ]
function rand(rng::AbstractRNG, s::PoissonCountSampler) μ = s.μ T = typeof(μ) n = 0 c = randexp(rng, T) while c < μ n += 1 c += randexp(rng, T) end return n end
function rand(rng::AbstractRNG, s::PoissonCountSampler) μ = s.μ T = typeof(μ) n = 0 c = randexp(rng, T) while c < μ n += 1 c += randexp(rng, T) end return n end
rand
22
32
src/samplers/poisson.jl
#FILE: Distributions.jl/src/univariate/discrete/skellam.jl ##CHUNK 1 function cdf(d::Skellam, t::Integer) μ1, μ2 = params(d) return if t < 0 nchisqcdf(-2*t, 2*μ1, 2*μ2) else 1 - nchisqcdf(2*(t+1), 2*μ2, 2*μ1) end end #### Sampling rand(rng::AbstractRNG, d::Skellam) = rand(rng, Poiss...
112
138
Distributions.jl
140
function procf(μ, K::Int, s) # can be pre-computed, but does not seem to affect performance ω = 0.3989422804014327/s b1 = 0.041666666666666664/μ b2 = 0.3*b1*b1 c3 = 0.14285714285714285*b1*b2 c2 = b2 - 15 * c3 c1 = b1 - 6 * b2 + 45 * c3 c0 = 1 - b1 + 3 * b2 - 15 * c3 if K < 10 ...
function procf(μ, K::Int, s) # can be pre-computed, but does not seem to affect performance ω = 0.3989422804014327/s b1 = 0.041666666666666664/μ b2 = 0.3*b1*b1 c3 = 0.14285714285714285*b1*b2 c2 = b2 - 15 * c3 c1 = b1 - 6 * b2 + 45 * c3 c0 = 1 - b1 + 3 * b2 - 15 * c3 if K < 10 ...
[ 112, 138 ]
function procf(μ, K::Int, s) # can be pre-computed, but does not seem to affect performance ω = 0.3989422804014327/s b1 = 0.041666666666666664/μ b2 = 0.3*b1*b1 c3 = 0.14285714285714285*b1*b2 c2 = b2 - 15 * c3 c1 = b1 - 6 * b2 + 45 * c3 c0 = 1 - b1 + 3 * b2 - 15 * c3 if K < 10 ...
function procf(μ, K::Int, s) # can be pre-computed, but does not seem to affect performance ω = 0.3989422804014327/s b1 = 0.041666666666666664/μ b2 = 0.3*b1*b1 c3 = 0.14285714285714285*b1*b2 c2 = b2 - 15 * c3 c1 = b1 - 6 * b2 + 45 * c3 c0 = 1 - b1 + 3 * b2 - 15 * c3 if K < 10 ...
procf
112
138
src/samplers/poisson.jl
#FILE: Distributions.jl/src/univariate/continuous/generalizedextremevalue.jl ##CHUNK 1 return σ^2 * (g(d, 2) - g(d, 1) ^ 2) / ξ^2 else return T(Inf) end end function skewness(d::GeneralizedExtremeValue{T}) where T<:Real (μ, σ, ξ) = params(d) if abs(ξ) < eps(one(ξ)) # ξ == 0 ret...
18
46
Distributions.jl
141
function rand(rng::AbstractRNG, s::VonMisesSampler) f = 0.0 local x::Float64 if s.κ > 700.0 x = s.μ + randn(rng) / sqrt(s.κ) else while true t, u = 0.0, 0.0 while true d = abs2(rand(rng) - 0.5) e = abs2(rand(rng) - 0.5) ...
function rand(rng::AbstractRNG, s::VonMisesSampler) f = 0.0 local x::Float64 if s.κ > 700.0 x = s.μ + randn(rng) / sqrt(s.κ) else while true t, u = 0.0, 0.0 while true d = abs2(rand(rng) - 0.5) e = abs2(rand(rng) - 0.5) ...
[ 18, 46 ]
function rand(rng::AbstractRNG, s::VonMisesSampler) f = 0.0 local x::Float64 if s.κ > 700.0 x = s.μ + randn(rng) / sqrt(s.κ) else while true t, u = 0.0, 0.0 while true d = abs2(rand(rng) - 0.5) e = abs2(rand(rng) - 0.5) ...
function rand(rng::AbstractRNG, s::VonMisesSampler) f = 0.0 local x::Float64 if s.κ > 700.0 x = s.μ + randn(rng) / sqrt(s.κ) else while true t, u = 0.0, 0.0 while true d = abs2(rand(rng) - 0.5) e = abs2(rand(rng) - 0.5) ...
rand
18
46
src/samplers/vonmises.jl
#FILE: Distributions.jl/src/truncated/normal.jl ##CHUNK 1 u = rand(rng) if u < exp(-0.5 * (r - a)^2) && r < ub return r end end elseif ub < 0 && ub - lb > 2.0 / (-ub + sqrt(ub^2 + 4.0)) * exp((ub^2 + ub * sqrt(ub^2 + 4.0)) / 4.0) ...
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Distributions.jl
142
function _rand!(rng::AbstractRNG, spl::VonMisesFisherSampler, x::AbstractVector) w = _vmf_genw(rng, spl) p = spl.p x[1] = w s = 0.0 @inbounds for i = 2:p x[i] = xi = randn(rng) s += abs2(xi) end # normalize x[2:p] r = sqrt((1.0 - abs2(w)) / s) @inbounds for i = 2:p ...
function _rand!(rng::AbstractRNG, spl::VonMisesFisherSampler, x::AbstractVector) w = _vmf_genw(rng, spl) p = spl.p x[1] = w s = 0.0 @inbounds for i = 2:p x[i] = xi = randn(rng) s += abs2(xi) end # normalize x[2:p] r = sqrt((1.0 - abs2(w)) / s) @inbounds for i = 2:p ...
[ 30, 47 ]
function _rand!(rng::AbstractRNG, spl::VonMisesFisherSampler, x::AbstractVector) w = _vmf_genw(rng, spl) p = spl.p x[1] = w s = 0.0 @inbounds for i = 2:p x[i] = xi = randn(rng) s += abs2(xi) end # normalize x[2:p] r = sqrt((1.0 - abs2(w)) / s) @inbounds for i = 2:p ...
function _rand!(rng::AbstractRNG, spl::VonMisesFisherSampler, x::AbstractVector) w = _vmf_genw(rng, spl) p = spl.p x[1] = w s = 0.0 @inbounds for i = 2:p x[i] = xi = randn(rng) s += abs2(xi) end # normalize x[2:p] r = sqrt((1.0 - abs2(w)) / s) @inbounds for i = 2:p ...
_rand!
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src/samplers/vonmisesfisher.jl
#FILE: Distributions.jl/test/multivariate/vonmisesfisher.jl ##CHUNK 1 end return X end function test_vmf_rot(p::Int, rng::Union{AbstractRNG, Missing} = missing) if ismissing(rng) μ = randn(p) x = randn(p) else μ = randn(rng, p) x = randn(rng, p) end κ = norm(μ) ...
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function _vmf_genwp(rng::AbstractRNG, p, b, x0, c, κ) r = (p - 1) / 2.0 betad = Beta(r, r) z = rand(rng, betad) w = (1.0 - (1.0 + b) * z) / (1.0 - (1.0 - b) * z) while κ * w + (p - 1) * log(1 - x0 * w) - c < log(rand(rng)) z = rand(rng, betad) w = (1.0 - (1.0 + b) * z) / (1.0 - (1.0 ...
function _vmf_genwp(rng::AbstractRNG, p, b, x0, c, κ) r = (p - 1) / 2.0 betad = Beta(r, r) z = rand(rng, betad) w = (1.0 - (1.0 + b) * z) / (1.0 - (1.0 - b) * z) while κ * w + (p - 1) * log(1 - x0 * w) - c < log(rand(rng)) z = rand(rng, betad) w = (1.0 - (1.0 + b) * z) / (1.0 - (1.0 ...
[ 59, 69 ]
function _vmf_genwp(rng::AbstractRNG, p, b, x0, c, κ) r = (p - 1) / 2.0 betad = Beta(r, r) z = rand(rng, betad) w = (1.0 - (1.0 + b) * z) / (1.0 - (1.0 - b) * z) while κ * w + (p - 1) * log(1 - x0 * w) - c < log(rand(rng)) z = rand(rng, betad) w = (1.0 - (1.0 + b) * z) / (1.0 - (1.0 ...
function _vmf_genwp(rng::AbstractRNG, p, b, x0, c, κ) r = (p - 1) / 2.0 betad = Beta(r, r) z = rand(rng, betad) w = (1.0 - (1.0 + b) * z) / (1.0 - (1.0 - b) * z) while κ * w + (p - 1) * log(1 - x0 * w) - c < log(rand(rng)) z = rand(rng, betad) w = (1.0 - (1.0 + b) * z) / (1.0 - (1.0 ...
_vmf_genwp
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src/samplers/vonmisesfisher.jl
#FILE: Distributions.jl/src/univariate/continuous/beta.jl ##CHUNK 1 if x + y ≤ one(x) if (x + y > 0) return x / (x + y) else logX = log(u) / α logY = log(v) / β logM = logX > logY ? logX : logY ...
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Distributions.jl
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function _vmf_householder_vec(μ::Vector{Float64}) # assuming μ is a unit-vector (which it should be) # can compute v in a single pass over μ p = length(μ) v = similar(μ) v[1] = μ[1] - 1.0 s = sqrt(-2*v[1]) v[1] /= s @inbounds for i in 2:p v[i] = μ[i] / s end return v ...
function _vmf_householder_vec(μ::Vector{Float64}) # assuming μ is a unit-vector (which it should be) # can compute v in a single pass over μ p = length(μ) v = similar(μ) v[1] = μ[1] - 1.0 s = sqrt(-2*v[1]) v[1] /= s @inbounds for i in 2:p v[i] = μ[i] / s end return v ...
[ 87, 102 ]
function _vmf_householder_vec(μ::Vector{Float64}) # assuming μ is a unit-vector (which it should be) # can compute v in a single pass over μ p = length(μ) v = similar(μ) v[1] = μ[1] - 1.0 s = sqrt(-2*v[1]) v[1] /= s @inbounds for i in 2:p v[i] = μ[i] / s end return v ...
function _vmf_householder_vec(μ::Vector{Float64}) # assuming μ is a unit-vector (which it should be) # can compute v in a single pass over μ p = length(μ) v = similar(μ) v[1] = μ[1] - 1.0 s = sqrt(-2*v[1]) v[1] /= s @inbounds for i in 2:p v[i] = μ[i] / s end return v ...
_vmf_householder_vec
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src/samplers/vonmisesfisher.jl
#FILE: Distributions.jl/test/multivariate/vonmisesfisher.jl ##CHUNK 1 end return X end function test_vmf_rot(p::Int, rng::Union{AbstractRNG, Missing} = missing) if ismissing(rng) μ = randn(p) x = randn(p) else μ = randn(rng, p) x = randn(rng, p) end κ = norm(μ) ...
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Distributions.jl
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function _tnmom1(a, b) mid = float(middle(a, b)) if !(a ≤ b) return oftype(mid, NaN) elseif a == b return mid elseif abs(a) > abs(b) return -_tnmom1(-b, -a) elseif isinf(a) && isinf(b) return zero(mid) end Δ = (b - a) * mid a′ = a * invsqrt2 b′ = b * i...
function _tnmom1(a, b) mid = float(middle(a, b)) if !(a ≤ b) return oftype(mid, NaN) elseif a == b return mid elseif abs(a) > abs(b) return -_tnmom1(-b, -a) elseif isinf(a) && isinf(b) return zero(mid) end Δ = (b - a) * mid a′ = a * invsqrt2 b′ = b * i...
[ 12, 34 ]
function _tnmom1(a, b) mid = float(middle(a, b)) if !(a ≤ b) return oftype(mid, NaN) elseif a == b return mid elseif abs(a) > abs(b) return -_tnmom1(-b, -a) elseif isinf(a) && isinf(b) return zero(mid) end Δ = (b - a) * mid a′ = a * invsqrt2 b′ = b * i...
function _tnmom1(a, b) mid = float(middle(a, b)) if !(a ≤ b) return oftype(mid, NaN) elseif a == b return mid elseif abs(a) > abs(b) return -_tnmom1(-b, -a) elseif isinf(a) && isinf(b) return zero(mid) end Δ = (b - a) * mid a′ = a * invsqrt2 b′ = b * i...
_tnmom1
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src/truncated/normal.jl
#FILE: Distributions.jl/src/univariate/continuous/triangular.jl ##CHUNK 1 res = (x - a)^2 / ((b - a) * (c - a)) return x < a ? zero(res) : res else res = 1 - (b - x)^2 / ((b - a) * (b - c)) return x ≥ b ? one(res) : res end end function quantile(d::TriangularDist, p::Real) (...
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function fit_mle(::Type{<:Beta}, x::AbstractArray{T}; maxiter::Int=1000, tol::Float64=1e-14) where T<:Real α₀,β₀ = params(fit(Beta,x)) #initial guess of parameters g₁ = mean(log.(x)) g₂ = mean(log.(one(T) .- x)) θ= [α₀ ; β₀ ] converged = false t=0 while !converged && t < maxiter #newto...
function fit_mle(::Type{<:Beta}, x::AbstractArray{T}; maxiter::Int=1000, tol::Float64=1e-14) where T<:Real α₀,β₀ = params(fit(Beta,x)) #initial guess of parameters g₁ = mean(log.(x)) g₂ = mean(log.(one(T) .- x)) θ= [α₀ ; β₀ ] converged = false t=0 while !converged && t < maxiter #newto...
[ 213, 237 ]
function fit_mle(::Type{<:Beta}, x::AbstractArray{T}; maxiter::Int=1000, tol::Float64=1e-14) where T<:Real α₀,β₀ = params(fit(Beta,x)) #initial guess of parameters g₁ = mean(log.(x)) g₂ = mean(log.(one(T) .- x)) θ= [α₀ ; β₀ ] converged = false t=0 while !converged && t < maxiter #newto...
function fit_mle(::Type{<:Beta}, x::AbstractArray{T}; maxiter::Int=1000, tol::Float64=1e-14) where T<:Real α₀,β₀ = params(fit(Beta,x)) #initial guess of parameters g₁ = mean(log.(x)) g₂ = mean(log.(one(T) .- x)) θ= [α₀ ; β₀ ] converged = false t=0 while !converged && t < maxiter #newto...
fit_mle
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src/univariate/continuous/beta.jl
#FILE: Distributions.jl/src/univariate/continuous/rician.jl ##CHUNK 1 function fit(::Type{<:Rician}, x::AbstractArray{T}; tol=1e-12, maxiters=500) where T μ₁ = mean(x) μ₂ = var(x) r = μ₁ / √μ₂ if r < sqrt(π/(4-π)) ν = zero(float(T)) σ = scale(fit(Rayleigh, x)) else ξ(θ) = 2 +...
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Distributions.jl
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function quantile(d::Chernoff, tau::Real) # some commonly used quantiles were precomputed precomputedquants=[ 0.0 -Inf; 0.01 -1.171534341573129; 0.025 -0.9981810946684274; 0.05 -0.8450811886357725; 0.1 -0.6642351964332931; 0.2 -0.43982766604886553; 0.25 -0...
function quantile(d::Chernoff, tau::Real) # some commonly used quantiles were precomputed precomputedquants=[ 0.0 -Inf; 0.01 -1.171534341573129; 0.025 -0.9981810946684274; 0.05 -0.8450811886357725; 0.1 -0.6642351964332931; 0.2 -0.43982766604886553; 0.25 -0...
[ 158, 200 ]
function quantile(d::Chernoff, tau::Real) # some commonly used quantiles were precomputed precomputedquants=[ 0.0 -Inf; 0.01 -1.171534341573129; 0.025 -0.9981810946684274; 0.05 -0.8450811886357725; 0.1 -0.6642351964332931; 0.2 -0.43982766604886553; 0.25 -0...
function quantile(d::Chernoff, tau::Real) # some commonly used quantiles were precomputed precomputedquants=[ 0.0 -Inf; 0.01 -1.171534341573129; 0.025 -0.9981810946684274; 0.05 -0.8450811886357725; 0.1 -0.6642351964332931; 0.2 -0.43982766604886553; 0.25 -0...
quantile
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src/univariate/continuous/chernoff.jl
#FILE: Distributions.jl/test/univariate/continuous/skewedexponentialpower.jl ##CHUNK 1 @testset "α != 0.5" begin # Format is [x, pdf, cdf] from the asymmetric # exponential power function in R from package # VaRES. Values are set to μ = 0, σ = 1, p = 0.5, α = 0.7 test = [ ...
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function rand(rng::AbstractRNG, d::Chernoff) # Ziggurat random number generator --- slow in the tails # constants needed for the Ziggurat algorithm A = 0.03248227216266608 x = [ 1.4765521793744492 1.3583996502410562 1.2788224934376338 1.2167121025431031 ...
function rand(rng::AbstractRNG, d::Chernoff) # Ziggurat random number generator --- slow in the tails # constants needed for the Ziggurat algorithm A = 0.03248227216266608 x = [ 1.4765521793744492 1.3583996502410562 1.2788224934376338 1.2167121025431031 ...
[ 217, 306 ]
function rand(rng::AbstractRNG, d::Chernoff) # Ziggurat random number generator --- slow in the tails # constants needed for the Ziggurat algorithm A = 0.03248227216266608 x = [ 1.4765521793744492 1.3583996502410562 1.2788224934376338 1.2167121025431031 ...
function rand(rng::AbstractRNG, d::Chernoff) # Ziggurat random number generator --- slow in the tails # constants needed for the Ziggurat algorithm A = 0.03248227216266608 x = [ 1.4765521793744492 1.3583996502410562 1.2788224934376338 1.2167121025431031 ...
rand
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src/univariate/continuous/chernoff.jl
#FILE: Distributions.jl/test/univariate/continuous/skewedexponentialpower.jl ##CHUNK 1 @testset "α != 0.5" begin # Format is [x, pdf, cdf] from the asymmetric # exponential power function in R from package # VaRES. Values are set to μ = 0, σ = 1, p = 0.5, α = 0.7 test = [ ...
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function logcdf(d::GeneralizedExtremeValue, x::Real) μ, σ, ξ = params(d) z = (x - μ) / σ return if abs(ξ) < eps(one(ξ)) # ξ == 0 -exp(- z) else # y(x) = y(bound) = 0 if x is not in the support with lower/upper bound y = max(1 + z * ξ, 0) - y^(-1/ξ) end end
function logcdf(d::GeneralizedExtremeValue, x::Real) μ, σ, ξ = params(d) z = (x - μ) / σ return if abs(ξ) < eps(one(ξ)) # ξ == 0 -exp(- z) else # y(x) = y(bound) = 0 if x is not in the support with lower/upper bound y = max(1 + z * ξ, 0) - y^(-1/ξ) end end
[ 223, 233 ]
function logcdf(d::GeneralizedExtremeValue, x::Real) μ, σ, ξ = params(d) z = (x - μ) / σ return if abs(ξ) < eps(one(ξ)) # ξ == 0 -exp(- z) else # y(x) = y(bound) = 0 if x is not in the support with lower/upper bound y = max(1 + z * ξ, 0) - y^(-1/ξ) end end
function logcdf(d::GeneralizedExtremeValue, x::Real) μ, σ, ξ = params(d) z = (x - μ) / σ return if abs(ξ) < eps(one(ξ)) # ξ == 0 -exp(- z) else # y(x) = y(bound) = 0 if x is not in the support with lower/upper bound y = max(1 + z * ξ, 0) - y^(-1/ξ) end end
logcdf
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src/univariate/continuous/generalizedextremevalue.jl
#FILE: Distributions.jl/src/univariate/continuous/generalizedpareto.jl ##CHUNK 1 # The logpdf is log(0) outside the support range. p = -T(Inf) if x >= μ z = (x - μ) / σ if abs(ξ) < eps() p = -z - log(σ) elseif ξ > 0 || (ξ < 0 && x < maximum(d)) p = (-1 - 1 / ...
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function rand(rng::AbstractRNG, d::GeneralizedExtremeValue) (μ, σ, ξ) = params(d) # Generate a Float64 random number uniformly in (0,1]. u = 1 - rand(rng) if abs(ξ) < eps(one(ξ)) # ξ == 0 rd = - log(- log(u)) else rd = expm1(- ξ * log(- log(u))) / ξ end return μ + σ * rd e...
function rand(rng::AbstractRNG, d::GeneralizedExtremeValue) (μ, σ, ξ) = params(d) # Generate a Float64 random number uniformly in (0,1]. u = 1 - rand(rng) if abs(ξ) < eps(one(ξ)) # ξ == 0 rd = - log(- log(u)) else rd = expm1(- ξ * log(- log(u))) / ξ end return μ + σ * rd e...
[ 241, 254 ]
function rand(rng::AbstractRNG, d::GeneralizedExtremeValue) (μ, σ, ξ) = params(d) # Generate a Float64 random number uniformly in (0,1]. u = 1 - rand(rng) if abs(ξ) < eps(one(ξ)) # ξ == 0 rd = - log(- log(u)) else rd = expm1(- ξ * log(- log(u))) / ξ end return μ + σ * rd e...
function rand(rng::AbstractRNG, d::GeneralizedExtremeValue) (μ, σ, ξ) = params(d) # Generate a Float64 random number uniformly in (0,1]. u = 1 - rand(rng) if abs(ξ) < eps(one(ξ)) # ξ == 0 rd = - log(- log(u)) else rd = expm1(- ξ * log(- log(u))) / ξ end return μ + σ * rd e...
rand
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src/univariate/continuous/generalizedextremevalue.jl
#FILE: Distributions.jl/src/univariate/continuous/generalizedpareto.jl ##CHUNK 1 end #### Sampling function rand(rng::AbstractRNG, d::GeneralizedPareto) # Generate a Float64 random number uniformly in (0,1]. u = 1 - rand(rng) if abs(d.ξ) < eps() rd = -log(u) else rd = expm1(-d.ξ * lo...
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Distributions.jl
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function logpdf(d::GeneralizedPareto{T}, x::Real) where T<:Real (μ, σ, ξ) = params(d) # The logpdf is log(0) outside the support range. p = -T(Inf) if x >= μ z = (x - μ) / σ if abs(ξ) < eps() p = -z - log(σ) elseif ξ > 0 || (ξ < 0 && x < maximum(d)) p = ...
function logpdf(d::GeneralizedPareto{T}, x::Real) where T<:Real (μ, σ, ξ) = params(d) # The logpdf is log(0) outside the support range. p = -T(Inf) if x >= μ z = (x - μ) / σ if abs(ξ) < eps() p = -z - log(σ) elseif ξ > 0 || (ξ < 0 && x < maximum(d)) p = ...
[ 128, 144 ]
function logpdf(d::GeneralizedPareto{T}, x::Real) where T<:Real (μ, σ, ξ) = params(d) # The logpdf is log(0) outside the support range. p = -T(Inf) if x >= μ z = (x - μ) / σ if abs(ξ) < eps() p = -z - log(σ) elseif ξ > 0 || (ξ < 0 && x < maximum(d)) p = ...
function logpdf(d::GeneralizedPareto{T}, x::Real) where T<:Real (μ, σ, ξ) = params(d) # The logpdf is log(0) outside the support range. p = -T(Inf) if x >= μ z = (x - μ) / σ if abs(ξ) < eps() p = -z - log(σ) elseif ξ > 0 || (ξ < 0 && x < maximum(d)) p = ...
logpdf
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src/univariate/continuous/generalizedpareto.jl
#FILE: Distributions.jl/src/univariate/continuous/generalizedextremevalue.jl ##CHUNK 1 function logpdf(d::GeneralizedExtremeValue{T}, x::Real) where T<:Real if x == -Inf || x == Inf || ! insupport(d, x) return -T(Inf) else (μ, σ, ξ) = params(d) z = (x - μ) / σ # Normalise x. if ab...
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function logccdf(d::GeneralizedPareto, x::Real) μ, σ, ξ = params(d) z = max((x - μ) / σ, 0) # z(x) = z(μ) = 0 if x < μ (lower bound) return if abs(ξ) < eps(one(ξ)) # ξ == 0 -z elseif ξ < 0 # y(x) = y(μ - σ / ξ) = -1 if x > μ - σ / ξ (upper bound) -log1p(max(z * ξ, -1)) / ξ el...
function logccdf(d::GeneralizedPareto, x::Real) μ, σ, ξ = params(d) z = max((x - μ) / σ, 0) # z(x) = z(μ) = 0 if x < μ (lower bound) return if abs(ξ) < eps(one(ξ)) # ξ == 0 -z elseif ξ < 0 # y(x) = y(μ - σ / ξ) = -1 if x > μ - σ / ξ (upper bound) -log1p(max(z * ξ, -1)) / ξ el...
[ 146, 157 ]
function logccdf(d::GeneralizedPareto, x::Real) μ, σ, ξ = params(d) z = max((x - μ) / σ, 0) # z(x) = z(μ) = 0 if x < μ (lower bound) return if abs(ξ) < eps(one(ξ)) # ξ == 0 -z elseif ξ < 0 # y(x) = y(μ - σ / ξ) = -1 if x > μ - σ / ξ (upper bound) -log1p(max(z * ξ, -1)) / ξ el...
function logccdf(d::GeneralizedPareto, x::Real) μ, σ, ξ = params(d) z = max((x - μ) / σ, 0) # z(x) = z(μ) = 0 if x < μ (lower bound) return if abs(ξ) < eps(one(ξ)) # ξ == 0 -z elseif ξ < 0 # y(x) = y(μ - σ / ξ) = -1 if x > μ - σ / ξ (upper bound) -log1p(max(z * ξ, -1)) / ξ el...
logccdf
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src/univariate/continuous/generalizedpareto.jl
#FILE: Distributions.jl/src/univariate/continuous/generalizedextremevalue.jl ##CHUNK 1 return (t * exp(-t)) / σ else if z * ξ == -1 # In this case: zero to the power something. return zero(T) else t = (1 + z*ξ)^(- 1 / ξ) return ...
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function quantile(d::GeneralizedPareto{T}, p::Real) where T<:Real (μ, σ, ξ) = params(d) if p == 0 z = zero(T) elseif p == 1 z = ξ < 0 ? -1 / ξ : T(Inf) elseif 0 < p < 1 if abs(ξ) < eps() z = -log1p(-p) else z = expm1(-ξ * log1p(-p)) / ξ en...
function quantile(d::GeneralizedPareto{T}, p::Real) where T<:Real (μ, σ, ξ) = params(d) if p == 0 z = zero(T) elseif p == 1 z = ξ < 0 ? -1 / ξ : T(Inf) elseif 0 < p < 1 if abs(ξ) < eps() z = -log1p(-p) else z = expm1(-ξ * log1p(-p)) / ξ en...
[ 163, 181 ]
function quantile(d::GeneralizedPareto{T}, p::Real) where T<:Real (μ, σ, ξ) = params(d) if p == 0 z = zero(T) elseif p == 1 z = ξ < 0 ? -1 / ξ : T(Inf) elseif 0 < p < 1 if abs(ξ) < eps() z = -log1p(-p) else z = expm1(-ξ * log1p(-p)) / ξ en...
function quantile(d::GeneralizedPareto{T}, p::Real) where T<:Real (μ, σ, ξ) = params(d) if p == 0 z = zero(T) elseif p == 1 z = ξ < 0 ? -1 / ξ : T(Inf) elseif 0 < p < 1 if abs(ξ) < eps() z = -log1p(-p) else z = expm1(-ξ * log1p(-p)) / ξ en...
quantile
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src/univariate/continuous/generalizedpareto.jl
#FILE: Distributions.jl/src/univariate/continuous/generalizedextremevalue.jl ##CHUNK 1 else if z * ξ == -1 # Otherwise, would compute zero to the power something. return -T(Inf) else t = (1 + z * ξ) ^ (-1/ξ) return - log(σ) + (ξ + 1) * log(...
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function rand(rng::AbstractRNG, d::GeneralizedPareto) # Generate a Float64 random number uniformly in (0,1]. u = 1 - rand(rng) if abs(d.ξ) < eps() rd = -log(u) else rd = expm1(-d.ξ * log(u)) / d.ξ end return d.μ + d.σ * rd end
function rand(rng::AbstractRNG, d::GeneralizedPareto) # Generate a Float64 random number uniformly in (0,1]. u = 1 - rand(rng) if abs(d.ξ) < eps() rd = -log(u) else rd = expm1(-d.ξ * log(u)) / d.ξ end return d.μ + d.σ * rd end
[ 186, 197 ]
function rand(rng::AbstractRNG, d::GeneralizedPareto) # Generate a Float64 random number uniformly in (0,1]. u = 1 - rand(rng) if abs(d.ξ) < eps() rd = -log(u) else rd = expm1(-d.ξ * log(u)) / d.ξ end return d.μ + d.σ * rd end
function rand(rng::AbstractRNG, d::GeneralizedPareto) # Generate a Float64 random number uniformly in (0,1]. u = 1 - rand(rng) if abs(d.ξ) < eps() rd = -log(u) else rd = expm1(-d.ξ * log(u)) / d.ξ end return d.μ + d.σ * rd end
rand
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src/univariate/continuous/generalizedpareto.jl
#FILE: Distributions.jl/src/univariate/continuous/generalizedextremevalue.jl ##CHUNK 1 function rand(rng::AbstractRNG, d::GeneralizedExtremeValue) (μ, σ, ξ) = params(d) # Generate a Float64 random number uniformly in (0,1]. u = 1 - rand(rng) if abs(ξ) < eps(one(ξ)) # ξ == 0 rd = - log(- log(u)...
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Distributions.jl
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function cdf(d::InverseGaussian, x::Real) μ, λ = params(d) y = max(x, 0) u = sqrt(λ / y) v = y / μ # 2λ/μ and normlogcdf(-u*(v+1)) are similar magnitude, opp. sign # truncating to [0, 1] as an additional precaution # Ref https://github.com/JuliaStats/Distributions.jl/issues/1873 z = clam...
function cdf(d::InverseGaussian, x::Real) μ, λ = params(d) y = max(x, 0) u = sqrt(λ / y) v = y / μ # 2λ/μ and normlogcdf(-u*(v+1)) are similar magnitude, opp. sign # truncating to [0, 1] as an additional precaution # Ref https://github.com/JuliaStats/Distributions.jl/issues/1873 z = clam...
[ 97, 109 ]
function cdf(d::InverseGaussian, x::Real) μ, λ = params(d) y = max(x, 0) u = sqrt(λ / y) v = y / μ # 2λ/μ and normlogcdf(-u*(v+1)) are similar magnitude, opp. sign # truncating to [0, 1] as an additional precaution # Ref https://github.com/JuliaStats/Distributions.jl/issues/1873 z = clam...
function cdf(d::InverseGaussian, x::Real) μ, λ = params(d) y = max(x, 0) u = sqrt(λ / y) v = y / μ # 2λ/μ and normlogcdf(-u*(v+1)) are similar magnitude, opp. sign # truncating to [0, 1] as an additional precaution # Ref https://github.com/JuliaStats/Distributions.jl/issues/1873 z = clam...
cdf
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src/univariate/continuous/inversegaussian.jl
#FILE: Distributions.jl/src/univariate/continuous/pgeneralizedgaussian.jl ##CHUNK 1 return ccdf(d, r) / 2 else return (1 + cdf(d, r)) / 2 end end function logcdf(d::PGeneralizedGaussian, x::Real) μ, α, p = params(d) return _normlogcdf_pgeneralizedgaussian(p, (x - μ) / α) end function lo...
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Distributions.jl
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function ccdf(d::InverseGaussian, x::Real) μ, λ = params(d) y = max(x, 0) u = sqrt(λ / y) v = y / μ # 2λ/μ and normlogcdf(-u*(v+1)) are similar magnitude, opp. sign # truncating to [0, 1] as an additional precaution # Ref https://github.com/JuliaStats/Distributions.jl/issues/1873 z = cla...
function ccdf(d::InverseGaussian, x::Real) μ, λ = params(d) y = max(x, 0) u = sqrt(λ / y) v = y / μ # 2λ/μ and normlogcdf(-u*(v+1)) are similar magnitude, opp. sign # truncating to [0, 1] as an additional precaution # Ref https://github.com/JuliaStats/Distributions.jl/issues/1873 z = cla...
[ 111, 123 ]
function ccdf(d::InverseGaussian, x::Real) μ, λ = params(d) y = max(x, 0) u = sqrt(λ / y) v = y / μ # 2λ/μ and normlogcdf(-u*(v+1)) are similar magnitude, opp. sign # truncating to [0, 1] as an additional precaution # Ref https://github.com/JuliaStats/Distributions.jl/issues/1873 z = cla...
function ccdf(d::InverseGaussian, x::Real) μ, λ = params(d) y = max(x, 0) u = sqrt(λ / y) v = y / μ # 2λ/μ and normlogcdf(-u*(v+1)) are similar magnitude, opp. sign # truncating to [0, 1] as an additional precaution # Ref https://github.com/JuliaStats/Distributions.jl/issues/1873 z = cla...
ccdf
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src/univariate/continuous/inversegaussian.jl
#FILE: Distributions.jl/src/univariate/continuous/pgeneralizedgaussian.jl ##CHUNK 1 function logccdf(d::PGeneralizedGaussian, x::Real) μ, α, p = params(d) return _normlogcdf_pgeneralizedgaussian(p, (μ - x) / α) end function _normlogcdf_pgeneralizedgaussian(p::Real, z::Real) r = abs(z)^p d = Gamma(inv(p)...
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Distributions.jl
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function logcdf(d::InverseGaussian, x::Real) μ, λ = params(d) y = max(x, 0) u = sqrt(λ / y) v = y / μ a = normlogcdf(u * (v - 1)) b = 2λ / μ + normlogcdf(-u * (v + 1)) z = logaddexp(a, b) # otherwise `NaN` is returned for `+Inf` return isinf(x) && x > 0 ? zero(z) : z end
function logcdf(d::InverseGaussian, x::Real) μ, λ = params(d) y = max(x, 0) u = sqrt(λ / y) v = y / μ a = normlogcdf(u * (v - 1)) b = 2λ / μ + normlogcdf(-u * (v + 1)) z = logaddexp(a, b) # otherwise `NaN` is returned for `+Inf` return isinf(x) && x > 0 ? zero(z) : z end
[ 125, 137 ]
function logcdf(d::InverseGaussian, x::Real) μ, λ = params(d) y = max(x, 0) u = sqrt(λ / y) v = y / μ a = normlogcdf(u * (v - 1)) b = 2λ / μ + normlogcdf(-u * (v + 1)) z = logaddexp(a, b) # otherwise `NaN` is returned for `+Inf` return isinf(x) && x > 0 ? zero(z) : z end
function logcdf(d::InverseGaussian, x::Real) μ, λ = params(d) y = max(x, 0) u = sqrt(λ / y) v = y / μ a = normlogcdf(u * (v - 1)) b = 2λ / μ + normlogcdf(-u * (v + 1)) z = logaddexp(a, b) # otherwise `NaN` is returned for `+Inf` return isinf(x) && x > 0 ? zero(z) : z end
logcdf
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src/univariate/continuous/inversegaussian.jl
#FILE: Distributions.jl/src/univariate/continuous/generalizedpareto.jl ##CHUNK 1 logcdf(d::GeneralizedPareto, x::Real) = log1mexp(logccdf(d, x)) function quantile(d::GeneralizedPareto{T}, p::Real) where T<:Real (μ, σ, ξ) = params(d) if p == 0 z = zero(T) elseif p == 1 z = ξ < 0 ? -1 / ξ : ...
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Distributions.jl
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function logccdf(d::InverseGaussian, x::Real) μ, λ = params(d) y = max(x, 0) u = sqrt(λ / y) v = y / μ a = normlogccdf(u * (v - 1)) b = 2λ / μ + normlogcdf(-u * (v + 1)) z = logsubexp(a, b) # otherwise `NaN` is returned for `+Inf` return isinf(x) && x > 0 ? oftype(z, -Inf) : z end
function logccdf(d::InverseGaussian, x::Real) μ, λ = params(d) y = max(x, 0) u = sqrt(λ / y) v = y / μ a = normlogccdf(u * (v - 1)) b = 2λ / μ + normlogcdf(-u * (v + 1)) z = logsubexp(a, b) # otherwise `NaN` is returned for `+Inf` return isinf(x) && x > 0 ? oftype(z, -Inf) : z end
[ 139, 151 ]
function logccdf(d::InverseGaussian, x::Real) μ, λ = params(d) y = max(x, 0) u = sqrt(λ / y) v = y / μ a = normlogccdf(u * (v - 1)) b = 2λ / μ + normlogcdf(-u * (v + 1)) z = logsubexp(a, b) # otherwise `NaN` is returned for `+Inf` return isinf(x) && x > 0 ? oftype(z, -Inf) : z end
function logccdf(d::InverseGaussian, x::Real) μ, λ = params(d) y = max(x, 0) u = sqrt(λ / y) v = y / μ a = normlogccdf(u * (v - 1)) b = 2λ / μ + normlogcdf(-u * (v + 1)) z = logsubexp(a, b) # otherwise `NaN` is returned for `+Inf` return isinf(x) && x > 0 ? oftype(z, -Inf) : z end
logccdf
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src/univariate/continuous/inversegaussian.jl
#FILE: Distributions.jl/src/univariate/continuous/generalizedpareto.jl ##CHUNK 1 logcdf(d::GeneralizedPareto, x::Real) = log1mexp(logccdf(d, x)) function quantile(d::GeneralizedPareto{T}, p::Real) where T<:Real (μ, σ, ξ) = params(d) if p == 0 z = zero(T) elseif p == 1 z = ξ < 0 ? -1 / ξ : ...
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Distributions.jl
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function _lambertwm1(x, n=6) if -exp(-one(x)) < x <= -1//4 β = -1 - sqrt2 * sqrt(1 + ℯ * x) elseif x < 0 lnmx = log(-x) β = lnmx - log(-lnmx) else throw(DomainError(x)) end for i in 1:n β = β / (1 + β) * (1 + log(x / β)) end return β end
function _lambertwm1(x, n=6) if -exp(-one(x)) < x <= -1//4 β = -1 - sqrt2 * sqrt(1 + ℯ * x) elseif x < 0 lnmx = log(-x) β = lnmx - log(-lnmx) else throw(DomainError(x)) end for i in 1:n β = β / (1 + β) * (1 + log(x / β)) end return β end
[ 143, 156 ]
function _lambertwm1(x, n=6) if -exp(-one(x)) < x <= -1//4 β = -1 - sqrt2 * sqrt(1 + ℯ * x) elseif x < 0 lnmx = log(-x) β = lnmx - log(-lnmx) else throw(DomainError(x)) end for i in 1:n β = β / (1 + β) * (1 + log(x / β)) end return β end
function _lambertwm1(x, n=6) if -exp(-one(x)) < x <= -1//4 β = -1 - sqrt2 * sqrt(1 + ℯ * x) elseif x < 0 lnmx = log(-x) β = lnmx - log(-lnmx) else throw(DomainError(x)) end for i in 1:n β = β / (1 + β) * (1 + log(x / β)) end return β end
_lambertwm1
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src/univariate/continuous/lindley.jl
#FILE: Distributions.jl/src/univariate/continuous/beta.jl ##CHUNK 1 iβ = s.iβ while true u = rand(rng) # the Uniform sampler just calls rand() v = rand(rng) x = u^iα y = v^iβ if x + y ≤ one(x) if (x + y > 0) ...
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Distributions.jl
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function fit_mle(::Type{<:Pareto}, x::AbstractArray{T}) where T<:Real # Based on # https://en.wikipedia.org/wiki/Pareto_distribution#Parameter_estimation θ = minimum(x) n = length(x) lθ = log(θ) temp1 = zero(T) for i=1:n temp1 += log(x[i]) - lθ end α = n/temp1 return P...
function fit_mle(::Type{<:Pareto}, x::AbstractArray{T}) where T<:Real # Based on # https://en.wikipedia.org/wiki/Pareto_distribution#Parameter_estimation θ = minimum(x) n = length(x) lθ = log(θ) temp1 = zero(T) for i=1:n temp1 += log(x[i]) - lθ end α = n/temp1 return P...
[ 124, 139 ]
function fit_mle(::Type{<:Pareto}, x::AbstractArray{T}) where T<:Real # Based on # https://en.wikipedia.org/wiki/Pareto_distribution#Parameter_estimation θ = minimum(x) n = length(x) lθ = log(θ) temp1 = zero(T) for i=1:n temp1 += log(x[i]) - lθ end α = n/temp1 return P...
function fit_mle(::Type{<:Pareto}, x::AbstractArray{T}) where T<:Real # Based on # https://en.wikipedia.org/wiki/Pareto_distribution#Parameter_estimation θ = minimum(x) n = length(x) lθ = log(θ) temp1 = zero(T) for i=1:n temp1 += log(x[i]) - lθ end α = n/temp1 return P...
fit_mle
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src/univariate/continuous/pareto.jl
#FILE: Distributions.jl/src/univariate/continuous/generalizedpareto.jl ##CHUNK 1 return T(Inf) end end #### Evaluation function logpdf(d::GeneralizedPareto{T}, x::Real) where T<:Real (μ, σ, ξ) = params(d) # The logpdf is log(0) outside the support range. p = -T(Inf) if x >= μ z ...
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Distributions.jl
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function pdf(d::TriangularDist, x::Real) a, b, c = params(d) res = if x < c 2 * (x - a) / ((b - a) * (c - a)) elseif x > c 2 * (b - x) / ((b - a) * (b - c)) else # Handle x == c separately to avoid `NaN` if `c == a` or `c == b` oftype(x - a, 2) / (b - a) end retur...
function pdf(d::TriangularDist, x::Real) a, b, c = params(d) res = if x < c 2 * (x - a) / ((b - a) * (c - a)) elseif x > c 2 * (b - x) / ((b - a) * (b - c)) else # Handle x == c separately to avoid `NaN` if `c == a` or `c == b` oftype(x - a, 2) / (b - a) end retur...
[ 94, 105 ]
function pdf(d::TriangularDist, x::Real) a, b, c = params(d) res = if x < c 2 * (x - a) / ((b - a) * (c - a)) elseif x > c 2 * (b - x) / ((b - a) * (b - c)) else # Handle x == c separately to avoid `NaN` if `c == a` or `c == b` oftype(x - a, 2) / (b - a) end retur...
function pdf(d::TriangularDist, x::Real) a, b, c = params(d) res = if x < c 2 * (x - a) / ((b - a) * (c - a)) elseif x > c 2 * (b - x) / ((b - a) * (b - c)) else # Handle x == c separately to avoid `NaN` if `c == a` or `c == b` oftype(x - a, 2) / (b - a) end retur...
pdf
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src/univariate/continuous/triangular.jl
#FILE: Distributions.jl/src/univariate/continuous/uniform.jl ##CHUNK 1 end function ccdf(d::Uniform, x::Real) a, b = params(d) return clamp((b - x) / (b - a), 0, 1) end quantile(d::Uniform, p::Real) = d.a + p * (d.b - d.a) cquantile(d::Uniform, p::Real) = d.b + p * (d.a - d.b) function mgf(d::Uniform, t::Rea...
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Distributions.jl
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function _vmcdf(κ::Real, I0κx::Real, x::Real, tol::Real) tol *= exp(-κ) j = 1 cj = besselix(j, κ) / j s = cj * sin(j * x) while abs(cj) > tol j += 1 cj = besselix(j, κ) / j s += cj * sin(j * x) end return (x + 2s / I0κx) / twoπ + 1//2 end
function _vmcdf(κ::Real, I0κx::Real, x::Real, tol::Real) tol *= exp(-κ) j = 1 cj = besselix(j, κ) / j s = cj * sin(j * x) while abs(cj) > tol j += 1 cj = besselix(j, κ) / j s += cj * sin(j * x) end return (x + 2s / I0κx) / twoπ + 1//2 end
[ 80, 91 ]
function _vmcdf(κ::Real, I0κx::Real, x::Real, tol::Real) tol *= exp(-κ) j = 1 cj = besselix(j, κ) / j s = cj * sin(j * x) while abs(cj) > tol j += 1 cj = besselix(j, κ) / j s += cj * sin(j * x) end return (x + 2s / I0κx) / twoπ + 1//2 end
function _vmcdf(κ::Real, I0κx::Real, x::Real, tol::Real) tol *= exp(-κ) j = 1 cj = besselix(j, κ) / j s = cj * sin(j * x) while abs(cj) > tol j += 1 cj = besselix(j, κ) / j s += cj * sin(j * x) end return (x + 2s / I0κx) / twoπ + 1//2 end
_vmcdf
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src/univariate/continuous/vonmises.jl
#FILE: Distributions.jl/src/samplers/vonmisesfisher.jl ##CHUNK 1 _vmf_bval(p::Int, κ::Real) = (p - 1) / (2.0κ + sqrt(4 * abs2(κ) + abs2(p - 1))) function _vmf_genw3(rng::AbstractRNG, p, b, x0, c, κ) ξ = rand(rng) w = 1.0 + (log(ξ + (1.0 - ξ)*exp(-2κ))/κ) return w::Float64 end function _vmf_genwp(rng::Abst...
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Distributions.jl
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function fit_mle(::Type{<:Weibull}, x::AbstractArray{<:Real}; alpha0::Real = 1, maxiter::Int = 1000, tol::Real = 1e-16) N = 0 lnx = map(log, x) lnxsq = lnx.^2 mean_lnx = mean(lnx) # first iteration outside loop, prevents type instability in α, ϵ xpow0 = x.^alpha0 sum_xpow0 = sum(xpow...
function fit_mle(::Type{<:Weibull}, x::AbstractArray{<:Real}; alpha0::Real = 1, maxiter::Int = 1000, tol::Real = 1e-16) N = 0 lnx = map(log, x) lnxsq = lnx.^2 mean_lnx = mean(lnx) # first iteration outside loop, prevents type instability in α, ϵ xpow0 = x.^alpha0 sum_xpow0 = sum(xpow...
[ 145, 187 ]
function fit_mle(::Type{<:Weibull}, x::AbstractArray{<:Real}; alpha0::Real = 1, maxiter::Int = 1000, tol::Real = 1e-16) N = 0 lnx = map(log, x) lnxsq = lnx.^2 mean_lnx = mean(lnx) # first iteration outside loop, prevents type instability in α, ϵ xpow0 = x.^alpha0 sum_xpow0 = sum(xpow...
function fit_mle(::Type{<:Weibull}, x::AbstractArray{<:Real}; alpha0::Real = 1, maxiter::Int = 1000, tol::Real = 1e-16) N = 0 lnx = map(log, x) lnxsq = lnx.^2 mean_lnx = mean(lnx) # first iteration outside loop, prevents type instability in α, ϵ xpow0 = x.^alpha0 sum_xpow0 = sum(xpow...
fit_mle
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src/univariate/continuous/weibull.jl
#FILE: Distributions.jl/src/univariate/continuous/rician.jl ##CHUNK 1 function fit(::Type{<:Rician}, x::AbstractArray{T}; tol=1e-12, maxiters=500) where T μ₁ = mean(x) μ₂ = var(x) r = μ₁ / √μ₂ if r < sqrt(π/(4-π)) ν = zero(float(T)) σ = scale(fit(Rayleigh, x)) else ξ(θ) = 2 +...
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Distributions.jl
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function kurtosis(d::BetaBinomial) n, α, β = d.n, d.α, d.β alpha_beta_sum = α + β alpha_beta_product = α * β numerator = ((alpha_beta_sum)^2) * (1 + alpha_beta_sum) denominator = (n * alpha_beta_product) * (alpha_beta_sum + 2) * (alpha_beta_sum + 3) * (alpha_beta_sum + n) left = numerator / deno...
function kurtosis(d::BetaBinomial) n, α, β = d.n, d.α, d.β alpha_beta_sum = α + β alpha_beta_product = α * β numerator = ((alpha_beta_sum)^2) * (1 + alpha_beta_sum) denominator = (n * alpha_beta_product) * (alpha_beta_sum + 2) * (alpha_beta_sum + 3) * (alpha_beta_sum + n) left = numerator / deno...
[ 72, 83 ]
function kurtosis(d::BetaBinomial) n, α, β = d.n, d.α, d.β alpha_beta_sum = α + β alpha_beta_product = α * β numerator = ((alpha_beta_sum)^2) * (1 + alpha_beta_sum) denominator = (n * alpha_beta_product) * (alpha_beta_sum + 2) * (alpha_beta_sum + 3) * (alpha_beta_sum + n) left = numerator / deno...
function kurtosis(d::BetaBinomial) n, α, β = d.n, d.α, d.β alpha_beta_sum = α + β alpha_beta_product = α * β numerator = ((alpha_beta_sum)^2) * (1 + alpha_beta_sum) denominator = (n * alpha_beta_product) * (alpha_beta_sum + 2) * (alpha_beta_sum + 3) * (alpha_beta_sum + n) left = numerator / deno...
kurtosis
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src/univariate/discrete/betabinomial.jl
#FILE: Distributions.jl/src/univariate/continuous/skewedexponentialpower.jl ##CHUNK 1 inv_p = inv(p) return k * (logtwo + inv_p * log(p) + log(σ)) + loggamma((1 + k) * inv_p) - loggamma(inv_p) + log(abs((-1)^k * α^(1 + k) + (1 - α)^(1 + k))) end # needed for odd moments in log scale sgn(d::SkewedExpon...
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Distributions.jl
165
function _pdf!(r::AbstractArray{<:Real}, d::Categorical{T}, rgn::UnitRange) where {T<:Real} vfirst = round(Int, first(rgn)) vlast = round(Int, last(rgn)) vl = max(vfirst, 1) vr = min(vlast, ncategories(d)) p = probs(d) if vl > vfirst for i = 1:(vl - vfirst) r[i] = zero(T) ...
function _pdf!(r::AbstractArray{<:Real}, d::Categorical{T}, rgn::UnitRange) where {T<:Real} vfirst = round(Int, first(rgn)) vlast = round(Int, last(rgn)) vl = max(vfirst, 1) vr = min(vlast, ncategories(d)) p = probs(d) if vl > vfirst for i = 1:(vl - vfirst) r[i] = zero(T) ...
[ 92, 113 ]
function _pdf!(r::AbstractArray{<:Real}, d::Categorical{T}, rgn::UnitRange) where {T<:Real} vfirst = round(Int, first(rgn)) vlast = round(Int, last(rgn)) vl = max(vfirst, 1) vr = min(vlast, ncategories(d)) p = probs(d) if vl > vfirst for i = 1:(vl - vfirst) r[i] = zero(T) ...
function _pdf!(r::AbstractArray{<:Real}, d::Categorical{T}, rgn::UnitRange) where {T<:Real} vfirst = round(Int, first(rgn)) vlast = round(Int, last(rgn)) vl = max(vfirst, 1) vr = min(vlast, ncategories(d)) p = probs(d) if vl > vfirst for i = 1:(vl - vfirst) r[i] = zero(T) ...
_pdf!
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src/univariate/discrete/categorical.jl
#FILE: Distributions.jl/src/univariates.jl ##CHUNK 1 r[v - fm1] = pdf(d, v) end return r end abstract type RecursiveProbabilityEvaluator end function _pdf!(r::AbstractArray, d::DiscreteUnivariateDistribution, X::UnitRange, rpe::RecursiveProbabilityEvaluator) vl,vr, vfirst, vlast = _pdf_fill_outsi...
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Distributions.jl
166
function rand(rng::AbstractRNG, d::DiscreteNonParametric) x = support(d) p = probs(d) n = length(p) draw = rand(rng, float(eltype(p))) cp = p[1] i = 1 while cp <= draw && i < n @inbounds cp += p[i +=1] end return x[i] end
function rand(rng::AbstractRNG, d::DiscreteNonParametric) x = support(d) p = probs(d) n = length(p) draw = rand(rng, float(eltype(p))) cp = p[1] i = 1 while cp <= draw && i < n @inbounds cp += p[i +=1] end return x[i] end
[ 76, 87 ]
function rand(rng::AbstractRNG, d::DiscreteNonParametric) x = support(d) p = probs(d) n = length(p) draw = rand(rng, float(eltype(p))) cp = p[1] i = 1 while cp <= draw && i < n @inbounds cp += p[i +=1] end return x[i] end
function rand(rng::AbstractRNG, d::DiscreteNonParametric) x = support(d) p = probs(d) n = length(p) draw = rand(rng, float(eltype(p))) cp = p[1] i = 1 while cp <= draw && i < n @inbounds cp += p[i +=1] end return x[i] end
rand
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src/univariate/discrete/discretenonparametric.jl
#FILE: Distributions.jl/src/multivariate/multinomial.jl ##CHUNK 1 n, p = params(d) s = -loggamma(n+1) + n*entropy(p) for pr in p b = Binomial(n, pr) for x in 0:n s += pdf(b, x) * loggamma(x+1) end end return s end # Evaluation function insupport(d::Multinomial,...
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Distributions.jl
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function cdf(d::DiscreteNonParametric, x::Real) ps = probs(d) P = float(eltype(ps)) # trivial cases x < minimum(d) && return zero(P) x >= maximum(d) && return one(P) isnan(x) && return P(NaN) n = length(ps) stop_idx = searchsortedlast(support(d), x) s = zero(P) if stop_idx < di...
function cdf(d::DiscreteNonParametric, x::Real) ps = probs(d) P = float(eltype(ps)) # trivial cases x < minimum(d) && return zero(P) x >= maximum(d) && return one(P) isnan(x) && return P(NaN) n = length(ps) stop_idx = searchsortedlast(support(d), x) s = zero(P) if stop_idx < di...
[ 112, 136 ]
function cdf(d::DiscreteNonParametric, x::Real) ps = probs(d) P = float(eltype(ps)) # trivial cases x < minimum(d) && return zero(P) x >= maximum(d) && return one(P) isnan(x) && return P(NaN) n = length(ps) stop_idx = searchsortedlast(support(d), x) s = zero(P) if stop_idx < di...
function cdf(d::DiscreteNonParametric, x::Real) ps = probs(d) P = float(eltype(ps)) # trivial cases x < minimum(d) && return zero(P) x >= maximum(d) && return one(P) isnan(x) && return P(NaN) n = length(ps) stop_idx = searchsortedlast(support(d), x) s = zero(P) if stop_idx < di...
cdf
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src/univariate/discrete/discretenonparametric.jl
#FILE: Distributions.jl/src/univariate/discrete/noncentralhypergeometric.jl ##CHUNK 1 function quantile(d::NoncentralHypergeometric{T}, q::Real) where T<:Real if !(zero(q) <= q <= one(q)) T(NaN) else range = support(d) if q > 1/2 q = 1 - q range = reverse(range) ...
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Distributions.jl
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function ccdf(d::DiscreteNonParametric, x::Real) ps = probs(d) P = float(eltype(ps)) # trivial cases x < minimum(d) && return one(P) x >= maximum(d) && return zero(P) isnan(x) && return P(NaN) n = length(ps) stop_idx = searchsortedlast(support(d), x) s = zero(P) if stop_idx < d...
function ccdf(d::DiscreteNonParametric, x::Real) ps = probs(d) P = float(eltype(ps)) # trivial cases x < minimum(d) && return one(P) x >= maximum(d) && return zero(P) isnan(x) && return P(NaN) n = length(ps) stop_idx = searchsortedlast(support(d), x) s = zero(P) if stop_idx < d...
[ 138, 162 ]
function ccdf(d::DiscreteNonParametric, x::Real) ps = probs(d) P = float(eltype(ps)) # trivial cases x < minimum(d) && return one(P) x >= maximum(d) && return zero(P) isnan(x) && return P(NaN) n = length(ps) stop_idx = searchsortedlast(support(d), x) s = zero(P) if stop_idx < d...
function ccdf(d::DiscreteNonParametric, x::Real) ps = probs(d) P = float(eltype(ps)) # trivial cases x < minimum(d) && return one(P) x >= maximum(d) && return zero(P) isnan(x) && return P(NaN) n = length(ps) stop_idx = searchsortedlast(support(d), x) s = zero(P) if stop_idx < d...
ccdf
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src/univariate/discrete/discretenonparametric.jl
#FILE: Distributions.jl/src/univariate/discrete/categorical.jl ##CHUNK 1 while cp < 1/2 && i <= k i += 1 @inbounds cp += p[i] end i end ### Evaluation # the fallbacks are overridden by `DiscreteNonParameteric` cdf(d::Categorical, x::Real) = cdf_int(d, x) ccdf(d::Categorical, x::Real) = ccd...
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Distributions.jl
169
function cdf(d::DiscreteUniform, x::Int) a = d.a result = (x - a + 1) * d.pv return if x < a zero(result) elseif x >= d.b one(result) else result end end
function cdf(d::DiscreteUniform, x::Int) a = d.a result = (x - a + 1) * d.pv return if x < a zero(result) elseif x >= d.b one(result) else result end end
[ 78, 88 ]
function cdf(d::DiscreteUniform, x::Int) a = d.a result = (x - a + 1) * d.pv return if x < a zero(result) elseif x >= d.b one(result) else result end end
function cdf(d::DiscreteUniform, x::Int) a = d.a result = (x - a + 1) * d.pv return if x < a zero(result) elseif x >= d.b one(result) else result end end
cdf
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src/univariate/discrete/discreteuniform.jl
#FILE: Distributions.jl/src/samplers/binomial.jl ##CHUNK 1 # compute probability vector of a Binomial distribution function binompvec(n::Int, p::Float64) pv = Vector{Float64}(undef, n+1) if p == 0.0 fill!(pv, 0.0) pv[1] = 1.0 elseif p == 1.0 fill!(pv, 0.0) pv[n+1] = 1.0 ...
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Distributions.jl
170
function logpdf(d::NegativeBinomial, k::Real) r, p = params(d) z = xlogy(r, p) + xlog1py(k, -p) if iszero(k) # in this case `logpdf(d, k) = z - log(k + r) - logbeta(r, k + 1) = z` analytically # but unfortunately not numerically, so we handle this case separately to improve accuracy ...
function logpdf(d::NegativeBinomial, k::Real) r, p = params(d) z = xlogy(r, p) + xlog1py(k, -p) if iszero(k) # in this case `logpdf(d, k) = z - log(k + r) - logbeta(r, k + 1) = z` analytically # but unfortunately not numerically, so we handle this case separately to improve accuracy ...
[ 97, 108 ]
function logpdf(d::NegativeBinomial, k::Real) r, p = params(d) z = xlogy(r, p) + xlog1py(k, -p) if iszero(k) # in this case `logpdf(d, k) = z - log(k + r) - logbeta(r, k + 1) = z` analytically # but unfortunately not numerically, so we handle this case separately to improve accuracy ...
function logpdf(d::NegativeBinomial, k::Real) r, p = params(d) z = xlogy(r, p) + xlog1py(k, -p) if iszero(k) # in this case `logpdf(d, k) = z - log(k + r) - logbeta(r, k + 1) = z` analytically # but unfortunately not numerically, so we handle this case separately to improve accuracy ...
logpdf
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src/univariate/discrete/negativebinomial.jl
#FILE: Distributions.jl/ext/DistributionsChainRulesCoreExt/univariate/discrete/negativebinomial.jl ##CHUNK 1 return ChainRulesCore.NoTangent(), Δd, ChainRulesCore.NoTangent() end function ChainRulesCore.rrule(::typeof(logpdf), d::NegativeBinomial, k::Real) # Compute log probability (as in the definition of `lo...
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Distributions.jl
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function pdf(d::FisherNoncentralHypergeometric, k::Integer) ω, _ = promote(d.ω, float(k)) l = max(0, d.n - d.nf) u = min(d.ns, d.n) if !insupport(d, k) return zero(ω) end η = mode(d) s = one(ω) fᵢ = one(ω) fₖ = one(ω) for i in (η + 1):u rᵢ = (d.ns - i + 1)*ω/(i*(d...
function pdf(d::FisherNoncentralHypergeometric, k::Integer) ω, _ = promote(d.ω, float(k)) l = max(0, d.n - d.nf) u = min(d.ns, d.n) if !insupport(d, k) return zero(ω) end η = mode(d) s = one(ω) fᵢ = one(ω) fₖ = one(ω) for i in (η + 1):u rᵢ = (d.ns - i + 1)*ω/(i*(d...
[ 85, 129 ]
function pdf(d::FisherNoncentralHypergeometric, k::Integer) ω, _ = promote(d.ω, float(k)) l = max(0, d.n - d.nf) u = min(d.ns, d.n) if !insupport(d, k) return zero(ω) end η = mode(d) s = one(ω) fᵢ = one(ω) fₖ = one(ω) for i in (η + 1):u rᵢ = (d.ns - i + 1)*ω/(i*(d...
function pdf(d::FisherNoncentralHypergeometric, k::Integer) ω, _ = promote(d.ω, float(k)) l = max(0, d.n - d.nf) u = min(d.ns, d.n) if !insupport(d, k) return zero(ω) end η = mode(d) s = one(ω) fᵢ = one(ω) fₖ = one(ω) for i in (η + 1):u rᵢ = (d.ns - i + 1)*ω/(i*(d...
pdf
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src/univariate/discrete/noncentralhypergeometric.jl
#FILE: Distributions.jl/src/univariate/continuous/rician.jl ##CHUNK 1 function fit(::Type{<:Rician}, x::AbstractArray{T}; tol=1e-12, maxiters=500) where T μ₁ = mean(x) μ₂ = var(x) r = μ₁ / √μ₂ if r < sqrt(π/(4-π)) ν = zero(float(T)) σ = scale(fit(Rayleigh, x)) else ξ(θ) = 2 +...
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Distributions.jl
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function cdf(d::FisherNoncentralHypergeometric, k::Integer) ω, _ = promote(d.ω, float(k)) l = max(0, d.n - d.nf) u = min(d.ns, d.n) if k < l return zero(ω) elseif k >= u return one(ω) end η = mode(d) s = one(ω) fᵢ = one(ω) Fₖ = k >= η ? one(ω) : zero(ω) for i ...
function cdf(d::FisherNoncentralHypergeometric, k::Integer) ω, _ = promote(d.ω, float(k)) l = max(0, d.n - d.nf) u = min(d.ns, d.n) if k < l return zero(ω) elseif k >= u return one(ω) end η = mode(d) s = one(ω) fᵢ = one(ω) Fₖ = k >= η ? one(ω) : zero(ω) for i ...
[ 133, 177 ]
function cdf(d::FisherNoncentralHypergeometric, k::Integer) ω, _ = promote(d.ω, float(k)) l = max(0, d.n - d.nf) u = min(d.ns, d.n) if k < l return zero(ω) elseif k >= u return one(ω) end η = mode(d) s = one(ω) fᵢ = one(ω) Fₖ = k >= η ? one(ω) : zero(ω) for i ...
function cdf(d::FisherNoncentralHypergeometric, k::Integer) ω, _ = promote(d.ω, float(k)) l = max(0, d.n - d.nf) u = min(d.ns, d.n) if k < l return zero(ω) elseif k >= u return one(ω) end η = mode(d) s = one(ω) fᵢ = one(ω) Fₖ = k >= η ? one(ω) : zero(ω) for i ...
cdf
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src/univariate/discrete/noncentralhypergeometric.jl
#FILE: Distributions.jl/src/univariate/continuous/rician.jl ##CHUNK 1 function fit(::Type{<:Rician}, x::AbstractArray{T}; tol=1e-12, maxiters=500) where T μ₁ = mean(x) μ₂ = var(x) r = μ₁ / √μ₂ if r < sqrt(π/(4-π)) ν = zero(float(T)) σ = scale(fit(Rayleigh, x)) else ξ(θ) = 2 +...
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Distributions.jl
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function _expectation(f, d::FisherNoncentralHypergeometric) ω = float(d.ω) l = max(0, d.n - d.nf) u = min(d.ns, d.n) η = mode(d) s = one(ω) m = f(η)*s fᵢ = one(ω) for i in (η + 1):u rᵢ = (d.ns - i + 1)*ω/(i*(d.nf - d.n + i))*(d.n - i + 1) fᵢ *= rᵢ # break if ter...
function _expectation(f, d::FisherNoncentralHypergeometric) ω = float(d.ω) l = max(0, d.n - d.nf) u = min(d.ns, d.n) η = mode(d) s = one(ω) m = f(η)*s fᵢ = one(ω) for i in (η + 1):u rᵢ = (d.ns - i + 1)*ω/(i*(d.nf - d.n + i))*(d.n - i + 1) fᵢ *= rᵢ # break if ter...
[ 179, 216 ]
function _expectation(f, d::FisherNoncentralHypergeometric) ω = float(d.ω) l = max(0, d.n - d.nf) u = min(d.ns, d.n) η = mode(d) s = one(ω) m = f(η)*s fᵢ = one(ω) for i in (η + 1):u rᵢ = (d.ns - i + 1)*ω/(i*(d.nf - d.n + i))*(d.n - i + 1) fᵢ *= rᵢ # break if ter...
function _expectation(f, d::FisherNoncentralHypergeometric) ω = float(d.ω) l = max(0, d.n - d.nf) u = min(d.ns, d.n) η = mode(d) s = one(ω) m = f(η)*s fᵢ = one(ω) for i in (η + 1):u rᵢ = (d.ns - i + 1)*ω/(i*(d.nf - d.n + i))*(d.n - i + 1) fᵢ *= rᵢ # break if ter...
_expectation
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src/univariate/discrete/noncentralhypergeometric.jl
#FILE: Distributions.jl/src/univariate/continuous/rician.jl ##CHUNK 1 function fit(::Type{<:Rician}, x::AbstractArray{T}; tol=1e-12, maxiters=500) where T μ₁ = mean(x) μ₂ = var(x) r = μ₁ / √μ₂ if r < sqrt(π/(4-π)) ν = zero(float(T)) σ = scale(fit(Rayleigh, x)) else ξ(θ) = 2 +...
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Distributions.jl
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function PoissonBinomial{T}(p::AbstractVector{T}; check_args::Bool=true) where {T <: Real} @check_args( PoissonBinomial, ( p, all(x -> zero(x) <= x <= one(x), p), "p must be a vector of success probabilities", ), ) ...
function PoissonBinomial{T}(p::AbstractVector{T}; check_args::Bool=true) where {T <: Real} @check_args( PoissonBinomial, ( p, all(x -> zero(x) <= x <= one(x), p), "p must be a vector of success probabilities", ), ) ...
[ 30, 40 ]
function PoissonBinomial{T}(p::AbstractVector{T}; check_args::Bool=true) where {T <: Real} @check_args( PoissonBinomial, ( p, all(x -> zero(x) <= x <= one(x), p), "p must be a vector of success probabilities", ), ) ...
function PoissonBinomial{T}(p::AbstractVector{T}; check_args::Bool=true) where {T <: Real} @check_args( PoissonBinomial, ( p, all(x -> zero(x) <= x <= one(x), p), "p must be a vector of success probabilities", ), ) ...
PoissonBinomial{T}
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src/univariate/discrete/poissonbinomial.jl
#FILE: Distributions.jl/src/univariate/discrete/negativebinomial.jl ##CHUNK 1 succprob(d) # Get the success rate, i.e. p failprob(d) # Get the failure rate, i.e. 1 - p ``` External links: * [Negative binomial distribution on Wolfram](https://reference.wolfram.com/language/ref/NegativeBinomialDistribution.html...
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Distributions.jl
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function poissonbinomial_pdf(p) S = zeros(eltype(p), length(p) + 1) S[1] = 1 @inbounds for (col, p_col) in enumerate(p) q_col = 1 - p_col for row in col:(-1):1 S[row + 1] = q_col * S[row + 1] + p_col * S[row] end S[1] *= q_col end return S end
function poissonbinomial_pdf(p) S = zeros(eltype(p), length(p) + 1) S[1] = 1 @inbounds for (col, p_col) in enumerate(p) q_col = 1 - p_col for row in col:(-1):1 S[row + 1] = q_col * S[row + 1] + p_col * S[row] end S[1] *= q_col end return S end
[ 153, 164 ]
function poissonbinomial_pdf(p) S = zeros(eltype(p), length(p) + 1) S[1] = 1 @inbounds for (col, p_col) in enumerate(p) q_col = 1 - p_col for row in col:(-1):1 S[row + 1] = q_col * S[row + 1] + p_col * S[row] end S[1] *= q_col end return S end
function poissonbinomial_pdf(p) S = zeros(eltype(p), length(p) + 1) S[1] = 1 @inbounds for (col, p_col) in enumerate(p) q_col = 1 - p_col for row in col:(-1):1 S[row + 1] = q_col * S[row + 1] + p_col * S[row] end S[1] *= q_col end return S end
poissonbinomial_pdf
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src/univariate/discrete/poissonbinomial.jl
#FILE: Distributions.jl/src/samplers/poisson.jl ##CHUNK 1 function poissonpvec(μ::Float64, n::Int) # Poisson probabilities, from 0 to n pv = Vector{Float64}(undef, n+1) @inbounds pv[1] = p = exp(-μ) for i = 1:n @inbounds pv[i+1] = (p *= (μ / i)) end return pv end #FILE: Distributions.j...
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Distributions.jl
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function poissonbinomial_pdf_partialderivatives(p::AbstractVector{<:Real}) n = length(p) A = zeros(eltype(p), n, n + 1) @inbounds for j in 1:n A[j, end] = 1 end @inbounds for (i, pi) in enumerate(p) qi = 1 - pi for k in (n - i + 1):n kp1 = k + 1 for j ...
function poissonbinomial_pdf_partialderivatives(p::AbstractVector{<:Real}) n = length(p) A = zeros(eltype(p), n, n + 1) @inbounds for j in 1:n A[j, end] = 1 end @inbounds for (i, pi) in enumerate(p) qi = 1 - pi for k in (n - i + 1):n kp1 = k + 1 for j ...
[ 222, 250 ]
function poissonbinomial_pdf_partialderivatives(p::AbstractVector{<:Real}) n = length(p) A = zeros(eltype(p), n, n + 1) @inbounds for j in 1:n A[j, end] = 1 end @inbounds for (i, pi) in enumerate(p) qi = 1 - pi for k in (n - i + 1):n kp1 = k + 1 for j ...
function poissonbinomial_pdf_partialderivatives(p::AbstractVector{<:Real}) n = length(p) A = zeros(eltype(p), n, n + 1) @inbounds for j in 1:n A[j, end] = 1 end @inbounds for (i, pi) in enumerate(p) qi = 1 - pi for k in (n - i + 1):n kp1 = k + 1 for j ...
poissonbinomial_pdf_partialderivatives
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src/univariate/discrete/poissonbinomial.jl
#FILE: Distributions.jl/src/multivariate/jointorderstatistics.jl ##CHUNK 1 issorted(x) && return lp return oftype(lp, -Inf) end i = first(ranks) xᵢ = first(x) if i > 1 # _marginalize_range(d.dist, 0, i, -Inf, xᵢ, T) lp += (i - 1) * logcdf(d.dist, xᵢ) - loggamma(T(i)) end ...
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QuantEcon.jl
177
function impulse_response(arma::ARMA; impulse_length=30) # Compute the impulse response function associated with ARMA process arma err_msg = "Impulse length must be greater than number of AR coefficients" @assert impulse_length >= arma.p err_msg # == Pad theta with zeros at the end == # theta = [arm...
function impulse_response(arma::ARMA; impulse_length=30) # Compute the impulse response function associated with ARMA process arma err_msg = "Impulse length must be greater than number of AR coefficients" @assert impulse_length >= arma.p err_msg # == Pad theta with zeros at the end == # theta = [arm...
[ 167, 182 ]
function impulse_response(arma::ARMA; impulse_length=30) # Compute the impulse response function associated with ARMA process arma err_msg = "Impulse length must be greater than number of AR coefficients" @assert impulse_length >= arma.p err_msg # == Pad theta with zeros at the end == # theta = [arm...
function impulse_response(arma::ARMA; impulse_length=30) # Compute the impulse response function associated with ARMA process arma err_msg = "Impulse length must be greater than number of AR coefficients" @assert impulse_length >= arma.p err_msg # == Pad theta with zeros at the end == # theta = [arm...
impulse_response
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src/arma.jl
#FILE: QuantEcon.jl/test/test_arma.jl ##CHUNK 1 @testset "Testing arma.jl" begin # set up phi = [.95, -.4, -.4] theta = zeros(3) sigma = .15 lp = ARMA(phi, theta, sigma) # test simulate sim = simulation(lp, ts_length=250) @test length(sim) == 250 # test impulse response imp_re...
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QuantEcon.jl
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function simulation(arma::ARMA; ts_length=90, impulse_length=30) # Simulate the ARMA process arma assuming Gaussian shocks J = impulse_length T = ts_length psi = impulse_response(arma, impulse_length=impulse_length) epsilon = arma.sigma * randn(T + J) X = Vector{Float64}(undef, T) for t=1:T ...
function simulation(arma::ARMA; ts_length=90, impulse_length=30) # Simulate the ARMA process arma assuming Gaussian shocks J = impulse_length T = ts_length psi = impulse_response(arma, impulse_length=impulse_length) epsilon = arma.sigma * randn(T + J) X = Vector{Float64}(undef, T) for t=1:T ...
[ 199, 210 ]
function simulation(arma::ARMA; ts_length=90, impulse_length=30) # Simulate the ARMA process arma assuming Gaussian shocks J = impulse_length T = ts_length psi = impulse_response(arma, impulse_length=impulse_length) epsilon = arma.sigma * randn(T + J) X = Vector{Float64}(undef, T) for t=1:T ...
function simulation(arma::ARMA; ts_length=90, impulse_length=30) # Simulate the ARMA process arma assuming Gaussian shocks J = impulse_length T = ts_length psi = impulse_response(arma, impulse_length=impulse_length) epsilon = arma.sigma * randn(T + J) X = Vector{Float64}(undef, T) for t=1:T ...
simulation
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src/arma.jl
#FILE: QuantEcon.jl/test/test_arma.jl ##CHUNK 1 @testset "Testing arma.jl" begin # set up phi = [.95, -.4, -.4] theta = zeros(3) sigma = .15 lp = ARMA(phi, theta, sigma) # test simulate sim = simulation(lp, ts_length=250) @test length(sim) == 250 # test impulse response imp_re...
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QuantEcon.jl
179
function compute_fixed_point(T::Function, v::TV; err_tol=1e-4, max_iter=100, verbose=2, print_skip=10) where TV if !(verbose in (0, 1, 2)) throw(ArgumentError("verbose...
function compute_fixed_point(T::Function, v::TV; err_tol=1e-4, max_iter=100, verbose=2, print_skip=10) where TV if !(verbose in (0, 1, 2)) throw(ArgumentError("verbose...
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function compute_fixed_point(T::Function, v::TV; err_tol=1e-4, max_iter=100, verbose=2, print_skip=10) where TV if !(verbose in (0, 1, 2)) throw(ArgumentError("verbose...
function compute_fixed_point(T::Function, v::TV; err_tol=1e-4, max_iter=100, verbose=2, print_skip=10) where TV if !(verbose in (0, 1, 2)) throw(ArgumentError("verbose...
compute_fixed_point
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src/compute_fp.jl
#FILE: QuantEcon.jl/test/test_compute_fp.jl ##CHUNK 1 @testset "Testing compute_fp.jl" begin # set up mu_1 = 0.2 # 0 is unique fixed point forall x_0 \in [0, 1] # (4mu - 1)/(4mu) is a fixed point forall x_0 \in [0, 1] mu_2 = 0.3 # starting points on (0, 1) unit_inverval = [0.1, 0.3, 0.6, 0.9...
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QuantEcon.jl
180
function smooth(x::Array, window_len::Int, window::AbstractString="hanning") if length(x) < window_len throw(ArgumentError("Input vector length must be >= window length")) end if window_len < 3 throw(ArgumentError("Window length must be at least 3.")) end if iseven(window_len) ...
function smooth(x::Array, window_len::Int, window::AbstractString="hanning") if length(x) < window_len throw(ArgumentError("Input vector length must be >= window length")) end if window_len < 3 throw(ArgumentError("Window length must be at least 3.")) end if iseven(window_len) ...
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function smooth(x::Array, window_len::Int, window::AbstractString="hanning") if length(x) < window_len throw(ArgumentError("Input vector length must be >= window length")) end if window_len < 3 throw(ArgumentError("Window length must be at least 3.")) end if iseven(window_len) ...
function smooth(x::Array, window_len::Int, window::AbstractString="hanning") if length(x) < window_len throw(ArgumentError("Input vector length must be >= window length")) end if window_len < 3 throw(ArgumentError("Window length must be at least 3.")) end if iseven(window_len) ...
smooth
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src/estspec.jl
#FILE: QuantEcon.jl/test/test_estspec.jl ##CHUNK 1 n_w, n_Iw, n_x = length(w), length(I_w), length(x) @test n_w == floor(Int, n_x / 2 + 1) @test n_Iw == floor(Int, n_x / 2 + 1) w, I_w = ar_periodogram(x) n_w, n_Iw, n_x = length(w), length(I_w), length(x) ...
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QuantEcon.jl
181
function periodogram(x::Vector) n = length(x) I_w = abs.(fft(x)).^2 ./ n w = 2pi * (0:n-1) ./ n # Fourier frequencies # int rounds to nearest integer. We want to round up or take 1/2 + 1 to # make sure we get the whole interval from [0, pi] ind = iseven(n) ? round(Int, n / 2 + 1) : ceil(Int, ...
function periodogram(x::Vector) n = length(x) I_w = abs.(fft(x)).^2 ./ n w = 2pi * (0:n-1) ./ n # Fourier frequencies # int rounds to nearest integer. We want to round up or take 1/2 + 1 to # make sure we get the whole interval from [0, pi] ind = iseven(n) ? round(Int, n / 2 + 1) : ceil(Int, ...
[ 74, 84 ]
function periodogram(x::Vector) n = length(x) I_w = abs.(fft(x)).^2 ./ n w = 2pi * (0:n-1) ./ n # Fourier frequencies # int rounds to nearest integer. We want to round up or take 1/2 + 1 to # make sure we get the whole interval from [0, pi] ind = iseven(n) ? round(Int, n / 2 + 1) : ceil(Int, ...
function periodogram(x::Vector) n = length(x) I_w = abs.(fft(x)).^2 ./ n w = 2pi * (0:n-1) ./ n # Fourier frequencies # int rounds to nearest integer. We want to round up or take 1/2 + 1 to # make sure we get the whole interval from [0, pi] ind = iseven(n) ? round(Int, n / 2 + 1) : ceil(Int, ...
periodogram
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src/estspec.jl
#FILE: QuantEcon.jl/test/test_estspec.jl ##CHUNK 1 @testset "Testing estspec" begin # set up x_20 = rand(20) x_21 = rand(21) @testset "testing output sizes of periodogram and ar_periodogram" begin # test shapes of periodogram and ar_periodogram functions for x in Any[x_20, x_21] ...
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QuantEcon.jl
182
function ar_periodogram(x::Array, window::AbstractString="hanning", window_len::Int=7) # run regression x_current, x_lagged = x[2:end], x[1:end-1] # x_t and x_{t-1} coefs = hcat(ones(size(x_lagged, 1)), x_lagged) \ x_current # get estimated values and compute residual est = [fill!(similar(x_lagge...
function ar_periodogram(x::Array, window::AbstractString="hanning", window_len::Int=7) # run regression x_current, x_lagged = x[2:end], x[1:end-1] # x_t and x_{t-1} coefs = hcat(ones(size(x_lagged, 1)), x_lagged) \ x_current # get estimated values and compute residual est = [fill!(similar(x_lagge...
[ 138, 157 ]
function ar_periodogram(x::Array, window::AbstractString="hanning", window_len::Int=7) # run regression x_current, x_lagged = x[2:end], x[1:end-1] # x_t and x_{t-1} coefs = hcat(ones(size(x_lagged, 1)), x_lagged) \ x_current # get estimated values and compute residual est = [fill!(similar(x_lagge...
function ar_periodogram(x::Array, window::AbstractString="hanning", window_len::Int=7) # run regression x_current, x_lagged = x[2:end], x[1:end-1] # x_t and x_{t-1} coefs = hcat(ones(size(x_lagged, 1)), x_lagged) \ x_current # get estimated values and compute residual est = [fill!(similar(x_lagge...
ar_periodogram
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src/estspec.jl
#FILE: QuantEcon.jl/src/filter.jl ##CHUNK 1 - `y_cycle::Vector` : cyclical component - `y_trend::Vector` : trend component """ function hamilton_filter(y::AbstractVector, h::Integer, p::Integer) y = Vector(y) T = length(y) y_cycle = fill(NaN, T) # construct X matrix of lags X = ones(T-p-h+1) fo...
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QuantEcon.jl
183
function hp_filter(y::AbstractVector{T}, λ::Real) where T <: Real y = Vector(y) N = length(y) H = spdiagm(-2 => fill(λ, N-2), -1 => vcat(-2λ, fill(-4λ, N - 3), -2λ), 0 => vcat(1 + λ, 1 + 5λ, fill(1 + 6λ, N-4), 1 + 5λ, 1 + λ), 1 => ...
function hp_filter(y::AbstractVector{T}, λ::Real) where T <: Real y = Vector(y) N = length(y) H = spdiagm(-2 => fill(λ, N-2), -1 => vcat(-2λ, fill(-4λ, N - 3), -2λ), 0 => vcat(1 + λ, 1 + 5λ, fill(1 + 6λ, N-4), 1 + 5λ, 1 + λ), 1 => ...
[ 12, 24 ]
function hp_filter(y::AbstractVector{T}, λ::Real) where T <: Real y = Vector(y) N = length(y) H = spdiagm(-2 => fill(λ, N-2), -1 => vcat(-2λ, fill(-4λ, N - 3), -2λ), 0 => vcat(1 + λ, 1 + 5λ, fill(1 + 6λ, N-4), 1 + 5λ, 1 + λ), 1 => ...
function hp_filter(y::AbstractVector{T}, λ::Real) where T <: Real y = Vector(y) N = length(y) H = spdiagm(-2 => fill(λ, N-2), -1 => vcat(-2λ, fill(-4λ, N - 3), -2λ), 0 => vcat(1 + λ, 1 + 5λ, fill(1 + 6λ, N-4), 1 + 5λ, 1 + λ), 1 => ...
hp_filter
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src/filter.jl
#FILE: QuantEcon.jl/src/markov/markov_approx.jl ##CHUNK 1 ##### Returns - `mc::MarkovChain` : Markov chain holding the state values and transition matrix """ function tauchen(N::Integer, ρ::T1, σ::T2, μ=zero(promote_type(T1, T2)), n_std::T3=3) where {T1 <: Real, T2 <: Real, T3 <: Real} # Get discretized space ...
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QuantEcon.jl
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function hamilton_filter(y::AbstractVector, h::Integer, p::Integer) y = Vector(y) T = length(y) y_cycle = fill(NaN, T) # construct X matrix of lags X = ones(T-p-h+1) for j = 1:p X = hcat(X, y[p-j+1:T-h-j+1]) end # do OLS regression b = (X'*X)\(X'*y[p+h:T]) y_cycle[p+h:T...
function hamilton_filter(y::AbstractVector, h::Integer, p::Integer) y = Vector(y) T = length(y) y_cycle = fill(NaN, T) # construct X matrix of lags X = ones(T-p-h+1) for j = 1:p X = hcat(X, y[p-j+1:T-h-j+1]) end # do OLS regression b = (X'*X)\(X'*y[p+h:T]) y_cycle[p+h:T...
[ 44, 60 ]
function hamilton_filter(y::AbstractVector, h::Integer, p::Integer) y = Vector(y) T = length(y) y_cycle = fill(NaN, T) # construct X matrix of lags X = ones(T-p-h+1) for j = 1:p X = hcat(X, y[p-j+1:T-h-j+1]) end # do OLS regression b = (X'*X)\(X'*y[p+h:T]) y_cycle[p+h:T...
function hamilton_filter(y::AbstractVector, h::Integer, p::Integer) y = Vector(y) T = length(y) y_cycle = fill(NaN, T) # construct X matrix of lags X = ones(T-p-h+1) for j = 1:p X = hcat(X, y[p-j+1:T-h-j+1]) end # do OLS regression b = (X'*X)\(X'*y[p+h:T]) y_cycle[p+h:T...
hamilton_filter
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src/filter.jl
#FILE: QuantEcon.jl/src/estspec.jl ##CHUNK 1 ##### Returns - `w::Array{Float64}`: Fourier frequencies at which the periodogram is evaluated - `I_w::Array{Float64}`: The periodogram at frequences `w` """ function ar_periodogram(x::Array, window::AbstractString="hanning", window_len::Int=7) # run regression x_...
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QuantEcon.jl
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function smooth(kn::Kalman, y::AbstractMatrix) G, R = kn.G, kn.R T = size(y, 2) n = kn.n x_filtered = Matrix{Float64}(undef, n, T) sigma_filtered = Array{Float64}(undef, n, n, T) sigma_forecast = Array{Float64}(undef, n, n, T) logL = 0 # forecast and update for t in 1:T logL...
function smooth(kn::Kalman, y::AbstractMatrix) G, R = kn.G, kn.R T = size(y, 2) n = kn.n x_filtered = Matrix{Float64}(undef, n, T) sigma_filtered = Array{Float64}(undef, n, n, T) sigma_forecast = Array{Float64}(undef, n, n, T) logL = 0 # forecast and update for t in 1:T logL...
[ 186, 214 ]
function smooth(kn::Kalman, y::AbstractMatrix) G, R = kn.G, kn.R T = size(y, 2) n = kn.n x_filtered = Matrix{Float64}(undef, n, T) sigma_filtered = Array{Float64}(undef, n, n, T) sigma_forecast = Array{Float64}(undef, n, n, T) logL = 0 # forecast and update for t in 1:T logL...
function smooth(kn::Kalman, y::AbstractMatrix) G, R = kn.G, kn.R T = size(y, 2) n = kn.n x_filtered = Matrix{Float64}(undef, n, T) sigma_filtered = Array{Float64}(undef, n, n, T) sigma_forecast = Array{Float64}(undef, n, n, T) logL = 0 # forecast and update for t in 1:T logL...
smooth
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src/kalman.jl
#FILE: QuantEcon.jl/test/test_kalman.jl ##CHUNK 1 curr_x, curr_sigma = fill(one(Float64), 2, 1), Matrix(I, 2, 2) .* .75 y_observed = fill(0.75, 2, 1) set_state!(kf, curr_x, curr_sigma) update!(kf, y_observed) mat_inv = inv(G * curr_sigma * G' + R) curr_k = A * curr_sigma * (G') * mat_inv new...
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QuantEcon.jl
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function stationary_values(lq::LQ) _lq = LQ(copy(lq.Q), copy(lq.R), copy(lq.A), copy(lq.B), copy(lq.C), copy(lq.N), bet=copy(lq.bet), capT=lq.capT, rf=copy(lq.rf)) stationary_values!(_lq) return _lq.P, _...
function stationary_values(lq::LQ) _lq = LQ(copy(lq.Q), copy(lq.R), copy(lq.A), copy(lq.B), copy(lq.C), copy(lq.N), bet=copy(lq.bet), capT=lq.capT, rf=copy(lq.rf)) stationary_values!(_lq) return _lq.P, _...
[ 221, 234 ]
function stationary_values(lq::LQ) _lq = LQ(copy(lq.Q), copy(lq.R), copy(lq.A), copy(lq.B), copy(lq.C), copy(lq.N), bet=copy(lq.bet), capT=lq.capT, rf=copy(lq.rf)) stationary_values!(_lq) return _lq.P, _...
function stationary_values(lq::LQ) _lq = LQ(copy(lq.Q), copy(lq.R), copy(lq.A), copy(lq.B), copy(lq.C), copy(lq.N), bet=copy(lq.bet), capT=lq.capT, rf=copy(lq.rf)) stationary_values!(_lq) return _lq.P, _...
stationary_values
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src/lqcontrol.jl
#FILE: QuantEcon.jl/src/robustlq.jl ##CHUNK 1 - `F::Matrix{Float64}` : The optimal control matrix from above - `P::Matrix{Float64}` : The positive semi-definite matrix defining the value function - `K::Matrix{Float64}` : the worst-case shock matrix ``K``, where ``w_{t+1} = K x_t`` is the worst case shock """ function...
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QuantEcon.jl
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function nnash(a, b1, b2, r1, r2, q1, q2, s1, s2, w1, w2, m1, m2; beta::Float64=1.0, tol::Float64=1e-8, max_iter::Int=1000) # Apply discounting a, b1, b2 = map(x->sqrt(beta) * x, Any[a, b1, b2]) dd = 10 its = 0 n = size(a, 1) # NOTE: if b1/b2 has 2 dimensions, this is exactly wh...
function nnash(a, b1, b2, r1, r2, q1, q2, s1, s2, w1, w2, m1, m2; beta::Float64=1.0, tol::Float64=1e-8, max_iter::Int=1000) # Apply discounting a, b1, b2 = map(x->sqrt(beta) * x, Any[a, b1, b2]) dd = 10 its = 0 n = size(a, 1) # NOTE: if b1/b2 has 2 dimensions, this is exactly wh...
[ 61, 116 ]
function nnash(a, b1, b2, r1, r2, q1, q2, s1, s2, w1, w2, m1, m2; beta::Float64=1.0, tol::Float64=1e-8, max_iter::Int=1000) # Apply discounting a, b1, b2 = map(x->sqrt(beta) * x, Any[a, b1, b2]) dd = 10 its = 0 n = size(a, 1) # NOTE: if b1/b2 has 2 dimensions, this is exactly wh...
function nnash(a, b1, b2, r1, r2, q1, q2, s1, s2, w1, w2, m1, m2; beta::Float64=1.0, tol::Float64=1e-8, max_iter::Int=1000) # Apply discounting a, b1, b2 = map(x->sqrt(beta) * x, Any[a, b1, b2]) dd = 10 its = 0 n = size(a, 1) # NOTE: if b1/b2 has 2 dimensions, this is exactly wh...
nnash
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src/lqnash.jl
#FILE: QuantEcon.jl/test/test_lqnash.jl ##CHUNK 1 0 d[1, 1]] q2 = [-0.5*e2[3] 0 0 d[2, 2]] s1 = zeros(2, 2) s2 = copy(s1) w1 = [0 0 0 0 -0.5*e1[2] B[1]/2.] w2 = [0 0 0 0 -0.5*e2[2] B[2]/2.] m1 = [0 0...
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QuantEcon.jl
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function simulate(lss::LSS, ts_length=100) x = Matrix{Float64}(undef, lss.n, ts_length) x[:, 1] = rand(lss.dist) w = randn(lss.m, ts_length - 1) v = randn(lss.l, ts_length) for t=1:ts_length-1 x[:, t+1] = lss.A * x[:, t] .+ lss.C * w[:, t] end y = lss.G * x + lss.H * v return x,...
function simulate(lss::LSS, ts_length=100) x = Matrix{Float64}(undef, lss.n, ts_length) x[:, 1] = rand(lss.dist) w = randn(lss.m, ts_length - 1) v = randn(lss.l, ts_length) for t=1:ts_length-1 x[:, t+1] = lss.A * x[:, t] .+ lss.C * w[:, t] end y = lss.G * x + lss.H * v return x,...
[ 97, 108 ]
function simulate(lss::LSS, ts_length=100) x = Matrix{Float64}(undef, lss.n, ts_length) x[:, 1] = rand(lss.dist) w = randn(lss.m, ts_length - 1) v = randn(lss.l, ts_length) for t=1:ts_length-1 x[:, t+1] = lss.A * x[:, t] .+ lss.C * w[:, t] end y = lss.G * x + lss.H * v return x,...
function simulate(lss::LSS, ts_length=100) x = Matrix{Float64}(undef, lss.n, ts_length) x[:, 1] = rand(lss.dist) w = randn(lss.m, ts_length - 1) v = randn(lss.l, ts_length) for t=1:ts_length-1 x[:, t+1] = lss.A * x[:, t] .+ lss.C * w[:, t] end y = lss.G * x + lss.H * v return x,...
simulate
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src/lss.jl
#FILE: QuantEcon.jl/test/test_lss.jl ##CHUNK 1 @test_throws ErrorException geometric_sums(sys, 0.97, rand(3)) end end @testset "test stability checks: stable systems" begin phi_0, phi_1, phi_2 = 1.1, 0.8, -0.8 A = [1.0 0.0 0 phi_0 phi_1 phi_2 0...
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function replicate(lss::LSS, t::Integer, num_reps::Integer=100) x = Matrix{Float64}(undef, lss.n, num_reps) v = randn(lss.l, num_reps) for j=1:num_reps x_t, _ = simulate(lss, t+1) x[:, j] = x_t[:, end] end y = lss.G * x + lss.H * v return x, y end
function replicate(lss::LSS, t::Integer, num_reps::Integer=100) x = Matrix{Float64}(undef, lss.n, num_reps) v = randn(lss.l, num_reps) for j=1:num_reps x_t, _ = simulate(lss, t+1) x[:, j] = x_t[:, end] end y = lss.G * x + lss.H * v return x, y end
[ 127, 137 ]
function replicate(lss::LSS, t::Integer, num_reps::Integer=100) x = Matrix{Float64}(undef, lss.n, num_reps) v = randn(lss.l, num_reps) for j=1:num_reps x_t, _ = simulate(lss, t+1) x[:, j] = x_t[:, end] end y = lss.G * x + lss.H * v return x, y end
function replicate(lss::LSS, t::Integer, num_reps::Integer=100) x = Matrix{Float64}(undef, lss.n, num_reps) v = randn(lss.l, num_reps) for j=1:num_reps x_t, _ = simulate(lss, t+1) x[:, j] = x_t[:, end] end y = lss.G * x + lss.H * v return x, y end
replicate
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src/lss.jl
#FILE: QuantEcon.jl/test/test_lss.jl ##CHUNK 1 @test_throws ErrorException geometric_sums(sys, 0.97, rand(3)) end end @testset "test stability checks: stable systems" begin phi_0, phi_1, phi_2 = 1.1, 0.8, -0.8 A = [1.0 0.0 0 phi_0 phi_1 phi_2 0...
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function Base.iterate(L::LSSMoments, state=(copy(L.lss.mu_0), copy(L.lss.Sigma_0))) A, C, G, H = L.lss.A, L.lss.C, L.lss.G, L.lss.H mu_x, Sigma_x = state mu_y, Sigma_y = G * mu_x, G * Sigma_x * G' + H * H' # Update moments of x mu_x2 = A * mu_x Sigma...
function Base.iterate(L::LSSMoments, state=(copy(L.lss.mu_0), copy(L.lss.Sigma_0))) A, C, G, H = L.lss.A, L.lss.C, L.lss.G, L.lss.H mu_x, Sigma_x = state mu_y, Sigma_y = G * mu_x, G * Sigma_x * G' + H * H' # Update moments of x mu_x2 = A * mu_x Sigma...
[ 146, 158 ]
function Base.iterate(L::LSSMoments, state=(copy(L.lss.mu_0), copy(L.lss.Sigma_0))) A, C, G, H = L.lss.A, L.lss.C, L.lss.G, L.lss.H mu_x, Sigma_x = state mu_y, Sigma_y = G * mu_x, G * Sigma_x * G' + H * H' # Update moments of x mu_x2 = A * mu_x Sigma...
function Base.iterate(L::LSSMoments, state=(copy(L.lss.mu_0), copy(L.lss.Sigma_0))) A, C, G, H = L.lss.A, L.lss.C, L.lss.G, L.lss.H mu_x, Sigma_x = state mu_y, Sigma_y = G * mu_x, G * Sigma_x * G' + H * H' # Update moments of x mu_x2 = A * mu_x Sigma...
Base.iterate
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src/lss.jl
#FILE: QuantEcon.jl/src/kalman.jl ##CHUNK 1 R k n cur_x_hat cur_sigma end # Initializes current mean and cov to zeros function Kalman(A, G, Q, R) k = size(G, 1) n = size(G, 2) xhat = n == 1 ? zero(eltype(A)) : zeros(n) Sigma = n == 1 ? zero(eltype(A)) : zeros(n, n) return Kalma...
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QuantEcon.jl
191
function remove_constants(lss::LSS) # Get size of matrix A = lss.A n, m = size(A) @assert n==m # Sum the absolute values of each row -> Do this because we # want to find rows that the sum of the absolute values is 1 row_sums_to_one = (vec(sum(abs, A, dims = 2) .- 1.0)) .< 1e-14 is_ii_on...
function remove_constants(lss::LSS) # Get size of matrix A = lss.A n, m = size(A) @assert n==m # Sum the absolute values of each row -> Do this because we # want to find rows that the sum of the absolute values is 1 row_sums_to_one = (vec(sum(abs, A, dims = 2) .- 1.0)) .< 1e-14 is_ii_on...
[ 266, 279 ]
function remove_constants(lss::LSS) # Get size of matrix A = lss.A n, m = size(A) @assert n==m # Sum the absolute values of each row -> Do this because we # want to find rows that the sum of the absolute values is 1 row_sums_to_one = (vec(sum(abs, A, dims = 2) .- 1.0)) .< 1e-14 is_ii_on...
function remove_constants(lss::LSS) # Get size of matrix A = lss.A n, m = size(A) @assert n==m # Sum the absolute values of each row -> Do this because we # want to find rows that the sum of the absolute values is 1 row_sums_to_one = (vec(sum(abs, A, dims = 2) .- 1.0)) .< 1e-14 is_ii_on...
remove_constants
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src/lss.jl
#FILE: QuantEcon.jl/test/test_lss.jl ##CHUNK 1 C = zeros(3, 1) G = [0.0 1.0 0.0] lss = LSS(A, C, G) lss2 = LSS(A[2:end, 2:end], C[2:end, :], G[:, 2:end]) # system without constant lss_vec = [lss, lss2] for sys in lss_vec @test is_stable(sys) == false ...
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QuantEcon.jl
192
function solve_discrete_lyapunov(A::ScalarOrArray, B::ScalarOrArray, max_it::Int=50) # TODO: Implement Bartels-Stewardt n = size(A, 2) alpha0 = reshape([A;], n, n) gamma0 = reshape([B;], n, n) alpha1 = fill!(similar(alpha0), zero(elt...
function solve_discrete_lyapunov(A::ScalarOrArray, B::ScalarOrArray, max_it::Int=50) # TODO: Implement Bartels-Stewardt n = size(A, 2) alpha0 = reshape([A;], n, n) gamma0 = reshape([B;], n, n) alpha1 = fill!(similar(alpha0), zero(elt...
[ 35, 66 ]
function solve_discrete_lyapunov(A::ScalarOrArray, B::ScalarOrArray, max_it::Int=50) # TODO: Implement Bartels-Stewardt n = size(A, 2) alpha0 = reshape([A;], n, n) gamma0 = reshape([B;], n, n) alpha1 = fill!(similar(alpha0), zero(elt...
function solve_discrete_lyapunov(A::ScalarOrArray, B::ScalarOrArray, max_it::Int=50) # TODO: Implement Bartels-Stewardt n = size(A, 2) alpha0 = reshape([A;], n, n) gamma0 = reshape([B;], n, n) alpha1 = fill!(similar(alpha0), zero(elt...
solve_discrete_lyapunov
35
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src/matrix_eqn.jl
#FILE: QuantEcon.jl/src/quadsums.jl ##CHUNK 1 """ function var_quadratic_sum(A::ScalarOrArray, C::ScalarOrArray, H::ScalarOrArray, bet::Real, x0::ScalarOrArray) n = size(A, 1) # coerce shapes A = reshape([A;], n, n) C = reshape([C;], n, n) H = reshape([H;], n, n) x0 ...
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QuantEcon.jl
193
function solve_discrete_riccati(A::ScalarOrArray, B::ScalarOrArray, Q::ScalarOrArray, R::ScalarOrArray, N::ScalarOrArray=zeros(size(R, 1), size(Q, 1)); tolerance::Float64=1e-10, ...
function solve_discrete_riccati(A::ScalarOrArray, B::ScalarOrArray, Q::ScalarOrArray, R::ScalarOrArray, N::ScalarOrArray=zeros(size(R, 1), size(Q, 1)); tolerance::Float64=1e-10, ...
[ 103, 177 ]
function solve_discrete_riccati(A::ScalarOrArray, B::ScalarOrArray, Q::ScalarOrArray, R::ScalarOrArray, N::ScalarOrArray=zeros(size(R, 1), size(Q, 1)); tolerance::Float64=1e-10, ...
function solve_discrete_riccati(A::ScalarOrArray, B::ScalarOrArray, Q::ScalarOrArray, R::ScalarOrArray, N::ScalarOrArray=zeros(size(R, 1), size(Q, 1)); tolerance::Float64=1e-10, ...
solve_discrete_riccati
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src/matrix_eqn.jl
#FILE: QuantEcon.jl/test/test_lqcontrol.jl ##CHUNK 1 r = 0.05 bet = 1 / (1 + r) t = 45 c_bar = 2.0 sigma = 0.25 mu = 1.0 q = 1e6 # == Formulate as an LQ problem == # Q = 1.0 R = zeros(2, 2) Rf = zeros(2, 2); Rf[1, 1] = q A ...
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QuantEcon.jl
194
function qnwlege(n::Int, a::Real, b::Real) maxit = 10000 m = fix((n + 1) / 2.0) xm = 0.5 * (b + a) xl = 0.5 * (b - a) nodes = zeros(n) weights = copy(nodes) i = 1:m z = cos.(pi * (i .- 0.25) ./ (n + 0.5)) # allocate memory for loop arrays p3 = similar(z) pp = similar(z) ...
function qnwlege(n::Int, a::Real, b::Real) maxit = 10000 m = fix((n + 1) / 2.0) xm = 0.5 * (b + a) xl = 0.5 * (b - a) nodes = zeros(n) weights = copy(nodes) i = 1:m z = cos.(pi * (i .- 0.25) ./ (n + 0.5)) # allocate memory for loop arrays p3 = similar(z) pp = similar(z) ...
[ 53, 102 ]
function qnwlege(n::Int, a::Real, b::Real) maxit = 10000 m = fix((n + 1) / 2.0) xm = 0.5 * (b + a) xl = 0.5 * (b - a) nodes = zeros(n) weights = copy(nodes) i = 1:m z = cos.(pi * (i .- 0.25) ./ (n + 0.5)) # allocate memory for loop arrays p3 = similar(z) pp = similar(z) ...
function qnwlege(n::Int, a::Real, b::Real) maxit = 10000 m = fix((n + 1) / 2.0) xm = 0.5 * (b + a) xl = 0.5 * (b - a) nodes = zeros(n) weights = copy(nodes) i = 1:m z = cos.(pi * (i .- 0.25) ./ (n + 0.5)) # allocate memory for loop arrays p3 = similar(z) pp = similar(z) ...
qnwlege
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src/quad.jl
#FILE: QuantEcon.jl/other/quadrature.jl ##CHUNK 1 p2 = 1 for j=2:n p3 = p2 p2 = p1 temp = 2 * j + ab aa = 2 * j * (j + ab) * (temp - 2) bb = (temp - 1) * (a * a - b * b + temp * (temp - 2) * z) c = 2 * (j - 1 + a...
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QuantEcon.jl
195
function qnwnorm(n::Int) maxit = 100 pim4 = 1 / pi^(0.25) m = floor(Int, (n + 1) / 2) nodes = zeros(n) weights = zeros(n) z = sqrt(2n + 1) - 1.85575 * ((2n + 1).^(-1 / 6)) for i = 1:m # Reasonable starting values for root finding if i == 1 z = sqrt(2n + 1) - 1.8...
function qnwnorm(n::Int) maxit = 100 pim4 = 1 / pi^(0.25) m = floor(Int, (n + 1) / 2) nodes = zeros(n) weights = zeros(n) z = sqrt(2n + 1) - 1.85575 * ((2n + 1).^(-1 / 6)) for i = 1:m # Reasonable starting values for root finding if i == 1 z = sqrt(2n + 1) - 1.8...
[ 158, 220 ]
function qnwnorm(n::Int) maxit = 100 pim4 = 1 / pi^(0.25) m = floor(Int, (n + 1) / 2) nodes = zeros(n) weights = zeros(n) z = sqrt(2n + 1) - 1.85575 * ((2n + 1).^(-1 / 6)) for i = 1:m # Reasonable starting values for root finding if i == 1 z = sqrt(2n + 1) - 1.8...
function qnwnorm(n::Int) maxit = 100 pim4 = 1 / pi^(0.25) m = floor(Int, (n + 1) / 2) nodes = zeros(n) weights = zeros(n) z = sqrt(2n + 1) - 1.85575 * ((2n + 1).^(-1 / 6)) for i = 1:m # Reasonable starting values for root finding if i == 1 z = sqrt(2n + 1) - 1.8...
qnwnorm
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src/quad.jl
#FILE: QuantEcon.jl/other/quadrature.jl ##CHUNK 1 r1 = (1 + 0.235b) / (0.766 + 0.119b) r2 = 1 / (1 + 0.639 * (n - 4) / (1 + 0.71 * (n - 4))) r3 = 1 / (1 + 20a / ((7.5+ a ) * n * n)) z = z + (z - x[n-3]) * r1 * r2 * r3 elseif i == n r1 = (1 + 0.37b) / ...
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QuantEcon.jl
196
function qnwsimp(n::Int, a::Real, b::Real) if n <= 1 error("In qnwsimp: n must be integer greater than one.") end if n % 2 == 0 @warn("In qnwsimp: n must be odd integer - increasing by 1.") n += 1 end dx = (b - a) / (n - 1) nodes = collect(a:dx:b) weights = repeat([...
function qnwsimp(n::Int, a::Real, b::Real) if n <= 1 error("In qnwsimp: n must be integer greater than one.") end if n % 2 == 0 @warn("In qnwsimp: n must be odd integer - increasing by 1.") n += 1 end dx = (b - a) / (n - 1) nodes = collect(a:dx:b) weights = repeat([...
[ 237, 255 ]
function qnwsimp(n::Int, a::Real, b::Real) if n <= 1 error("In qnwsimp: n must be integer greater than one.") end if n % 2 == 0 @warn("In qnwsimp: n must be odd integer - increasing by 1.") n += 1 end dx = (b - a) / (n - 1) nodes = collect(a:dx:b) weights = repeat([...
function qnwsimp(n::Int, a::Real, b::Real) if n <= 1 error("In qnwsimp: n must be integer greater than one.") end if n % 2 == 0 @warn("In qnwsimp: n must be odd integer - increasing by 1.") n += 1 end dx = (b - a) / (n - 1) nodes = collect(a:dx:b) weights = repeat([...
qnwsimp
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src/quad.jl
#CURRENT FILE: QuantEcon.jl/src/quad.jl ##CHUNK 1 if abs(z - z1) < 1e-14 break end end if it >= maxit error("Failed to converge in qnwnorm") end nodes[n + 1 - i] = z nodes[i] = -z weights[i] = 2 ./ (pp .* pp) w...
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QuantEcon.jl
197
function qnwtrap(n::Int, a::Real, b::Real) if n < 1 error("n must be at least 1") end dx = (b - a) / (n - 1) nodes = collect(a:dx:b) weights = fill(dx, n) weights[[1, n]] .*= 0.5 return nodes, weights end
function qnwtrap(n::Int, a::Real, b::Real) if n < 1 error("n must be at least 1") end dx = (b - a) / (n - 1) nodes = collect(a:dx:b) weights = fill(dx, n) weights[[1, n]] .*= 0.5 return nodes, weights end
[ 272, 282 ]
function qnwtrap(n::Int, a::Real, b::Real) if n < 1 error("n must be at least 1") end dx = (b - a) / (n - 1) nodes = collect(a:dx:b) weights = fill(dx, n) weights[[1, n]] .*= 0.5 return nodes, weights end
function qnwtrap(n::Int, a::Real, b::Real) if n < 1 error("n must be at least 1") end dx = (b - a) / (n - 1) nodes = collect(a:dx:b) weights = fill(dx, n) weights[[1, n]] .*= 0.5 return nodes, weights end
qnwtrap
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src/quad.jl
#CURRENT FILE: QuantEcon.jl/src/quad.jl ##CHUNK 1 if n % 2 == 0 @warn("In qnwsimp: n must be odd integer - increasing by 1.") n += 1 end dx = (b - a) / (n - 1) nodes = collect(a:dx:b) weights = repeat([2.0, 4.0], Int((n + 1) / 2)) weights = weights[1:n] weights[1] = 1 w...
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QuantEcon.jl
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function qnwbeta(n::Int, a::Real, b::Real) a -= 1 b -= 1 ab = a + b maxit = 25 x = zeros(n) w = zeros(n) z::Float64 = 0.0 for i = 1:n if i == 1 an = a / n bn = b / n r1 = (1 + a) * (2.78 / (4 + n * n) + 0.768an / n) r2 = 1 + 1.4...
function qnwbeta(n::Int, a::Real, b::Real) a -= 1 b -= 1 ab = a + b maxit = 25 x = zeros(n) w = zeros(n) z::Float64 = 0.0 for i = 1:n if i == 1 an = a / n bn = b / n r1 = (1 + a) * (2.78 / (4 + n * n) + 0.768an / n) r2 = 1 + 1.4...
[ 301, 391 ]
function qnwbeta(n::Int, a::Real, b::Real) a -= 1 b -= 1 ab = a + b maxit = 25 x = zeros(n) w = zeros(n) z::Float64 = 0.0 for i = 1:n if i == 1 an = a / n bn = b / n r1 = (1 + a) * (2.78 / (4 + n * n) + 0.768an / n) r2 = 1 + 1.4...
function qnwbeta(n::Int, a::Real, b::Real) a -= 1 b -= 1 ab = a + b maxit = 25 x = zeros(n) w = zeros(n) z::Float64 = 0.0 for i = 1:n if i == 1 an = a / n bn = b / n r1 = (1 + a) * (2.78 / (4 + n * n) + 0.768an / n) r2 = 1 + 1.4...
qnwbeta
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src/quad.jl
#FILE: QuantEcon.jl/other/quadrature.jl ##CHUNK 1 if i == 1 an = a / n bn = b / n r1 = (1 + a) * (2.78 / (4 + n * n) + 0.768an / n) r2 = 1 + 1.48 * an + 0.96bn + 0.452an*an + 0.83an*bn z = 1 - r1 / r2 elseif i == 2 r1 = (4.1 + a) /...
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QuantEcon.jl
199
function qnwgamma(n::Int, a::Real = 1.0, b::Real = 1.0) a < 0 && error("shape parameter must be positive") b < 0 && error("scale parameter must be positive") a -= 1 maxit = 25 fact = -exp((logabsgamma(a + n))[1] - (logabsgamma(n))[1] - (logabsgamma(a + 1))[1] ) nodes = zeros(n) weights = ze...
function qnwgamma(n::Int, a::Real = 1.0, b::Real = 1.0) a < 0 && error("shape parameter must be positive") b < 0 && error("scale parameter must be positive") a -= 1 maxit = 25 fact = -exp((logabsgamma(a + n))[1] - (logabsgamma(n))[1] - (logabsgamma(a + 1))[1] ) nodes = zeros(n) weights = ze...
[ 410, 464 ]
function qnwgamma(n::Int, a::Real = 1.0, b::Real = 1.0) a < 0 && error("shape parameter must be positive") b < 0 && error("scale parameter must be positive") a -= 1 maxit = 25 fact = -exp((logabsgamma(a + n))[1] - (logabsgamma(n))[1] - (logabsgamma(a + 1))[1] ) nodes = zeros(n) weights = ze...
function qnwgamma(n::Int, a::Real = 1.0, b::Real = 1.0) a < 0 && error("shape parameter must be positive") b < 0 && error("scale parameter must be positive") a -= 1 maxit = 25 fact = -exp((logabsgamma(a + n))[1] - (logabsgamma(n))[1] - (logabsgamma(a + 1))[1] ) nodes = zeros(n) weights = ze...
qnwgamma
410
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src/quad.jl
#FILE: QuantEcon.jl/other/quadrature.jl ##CHUNK 1 function qnwbeta(n::Int, a::T, b::S) where {T <: Real, S <: Real} a -= 1 b -= 1 maxit = 25 x = zeros(n) w = zeros(n) for i=1:n if i == 1 an = a / n bn = b / n r1 = (1 + a) * (2.78 / (4 + n * n) + 0.7...