From 8f927ce48d2853bf0f5e675f9b7d1eeb190df234 Mon Sep 17 00:00:00 2001
From: Jack Li <yli566@ucsc.edu>
Date: Tue, 19 Sep 2023 15:53:34 -0400
Subject: [PATCH 01/13] add loglogistic distribution

---
 docs/Project.toml                         |   1 +
 docs/src/univariate.md                    |  11 +-
 src/Distributions.jl                      |   3 +-
 src/univariate/continuous/loglogistic.jl  | 142 ++++++++++++++++++++++
 src/univariates.jl                        |   1 +
 test/runtests.jl                          |   2 +
 test/univariate/continuous/loglogistic.jl |  25 ++++
 7 files changed, 182 insertions(+), 3 deletions(-)
 create mode 100644 src/univariate/continuous/loglogistic.jl
 create mode 100644 test/univariate/continuous/loglogistic.jl

diff --git a/docs/Project.toml b/docs/Project.toml
index 540725c6d6..2ef490a4d9 100644
--- a/docs/Project.toml
+++ b/docs/Project.toml
@@ -1,4 +1,5 @@
 [deps]
+Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
 GR = "28b8d3ca-fb5f-59d9-8090-bfdbd6d07a71"
 
diff --git a/docs/src/univariate.md b/docs/src/univariate.md
index 0b2c48c6ea..62c53dd644 100644
--- a/docs/src/univariate.md
+++ b/docs/src/univariate.md
@@ -320,10 +320,17 @@ plotdensity((0, 20), Lindley, (1.5,)) # hide
 ```
 
 ```@docs
-Logistic
+logistic
 ```
 ```@example plotdensity
-plotdensity((-4, 8), Logistic, (2, 1)) # hide
+plotdensity((-4, 8), logistic, (2, 1)) # hide
+```
+
+```@docs
+loglogistic
+```
+```@example plotdensity
+plotdensity((0, 2), logistic, (1, 1)) # hide
 ```
 
 ```@docs
diff --git a/src/Distributions.jl b/src/Distributions.jl
index 1e2d580c55..39b3ec1196 100644
--- a/src/Distributions.jl
+++ b/src/Distributions.jl
@@ -120,6 +120,7 @@ export
     LKJCholesky,
     LocationScale,
     Logistic,
+    LogLogistic,
     LogNormal,
     LogUniform,
     LogitNormal,
@@ -356,7 +357,7 @@ Supported distributions:
     InverseWishart, InverseGamma, InverseGaussian, IsoNormal,
     IsoNormalCanon, JohnsonSU, Kolmogorov, KSDist, KSOneSided, Kumaraswamy,
     Laplace, Levy, Lindley, LKJ, LKJCholesky,
-    Logistic, LogNormal, MatrixBeta, MatrixFDist, MatrixNormal,
+    Logistic, LogLogistic, LogNormal, MatrixBeta, MatrixFDist, MatrixNormal,
     MatrixTDist, MixtureModel, Multinomial,
     MultivariateNormal, MvLogNormal, MvNormal, MvNormalCanon,
     MvNormalKnownCov, MvTDist, NegativeBinomial, NoncentralBeta, NoncentralChisq,
diff --git a/src/univariate/continuous/loglogistic.jl b/src/univariate/continuous/loglogistic.jl
new file mode 100644
index 0000000000..806ede8808
--- /dev/null
+++ b/src/univariate/continuous/loglogistic.jl
@@ -0,0 +1,142 @@
+"""
+    LogLogistic(θ, ϕ)
+
+The *log logistic distribution* with scale `θ` and shape `ϕ` is the distribution of a random variable whose logarithm has a [`Logistic`](@ref) distribution. 
+If ``X \\sim \\operatorname{Logistic}(\\theta, \\phi)`` then ``exp(X) \\sim \\operatorname{LogLogistic}(\\theta, \\phi)``. The probability density function is 
+
+```math
+f(x; \\theta, \\phi) = \\frac{(\\phi / \\theta)x/\\theta()^(\\phi - 1)}{(1 + (x/\\theta)^\\phi)^2}, \\theta > 0, \\phi > 0
+```
+
+```julia
+LogLogistic()            # Log-logistic distribution with unit scale and unit shape
+LogLogistic(θ)           # Log-logistic distribution with scale θ and unit shape
+LogLogistic(θ,ϕ)         # Log-logistic distribution with scale θ and shape ϕ
+
+params(d)                # Get the parameters, i.e. (θ, ϕ)
+scale(d)                 # Get the scale parameter, i.e. θ
+shape(d)                 # Get the shape parameter, i.e. ϕ
+```
+
+External links
+
+* [Log logistic distribution on Wikipedia](https://en.wikipedia.org/wiki/Log-logistic_distribution)
+
+"""
+
+
+struct LogLogistic{T<:Real} <: ContinuousUnivariateDistribution
+    θ::T
+    ϕ::T
+    LogLogistic{T}(θ::T,ϕ::T) where {T} = new{T}(θ,ϕ)
+end
+
+function LogLogistic(θ::T, ϕ::T; check_args=true) where {T <: Real}
+    check_args && @check_args(LogLogistic, θ > zero(θ) && ϕ > zero(ϕ))
+    return LogLogistic{T}(θ, ϕ)
+end
+
+LogLogistic(θ::Real, ϕ::Real) = LogLogistic(promote(θ,ϕ)...)
+LogLogistic(θ::Integer, ϕ::Integer) = LogLogistic(float(θ), float(ϕ))
+LogLogistic(θ::T) where {T<:Real} = LogLogistic(θ, 1.0)
+LogLogistic() = LogLogistic(1.0, 1.0, check_args=false) 
+
+@distr_support LogLogistic 0.0 Inf
+
+#### Coversions
+convert(::Type{LogLogistic{T}}, θ::S, ϕ::S) where {T <: Real, S <: Real} = LogLogistic(T(θ), T(ϕ))
+convert(::Type{LogLogistic{T}}, d::LogLogistic{S}) where {T <: Real, S <: Real} = LogLogistic(T(d.θ), T(d.ϕ), check_args=false)
+
+#### Parameters 
+
+params(d::LogLogistic) = (d.θ, d.ϕ)
+partype(::LogLogistic{T}) where {T} = T
+
+#### Statistics 
+
+median(d::LogLogistic) = d.θ
+function mean(d::LogLogistic)
+	if d.ϕ ≤ 1
+        error("mean is defined only when ϕ > 1") 	
+	end
+	return d.θ*π/d.ϕ/sin(π/d.ϕ)
+end
+
+function mode(d::LogLogistic)
+	if d.ϕ ≤ 1
+		error("mode is defined only when ϕ > 1")
+	end 
+	return d.θ*((d.ϕ-1)/(d.ϕ+1))^(1/d.ϕ)
+end
+
+function var(d::LogLogistic)
+	if d.ϕ ≤ 2
+		erros("var is defined only when ϕ > 2") 
+	end
+    b = π/d.ϕ
+	return d.θ^2 * (2*b/sin(2*b)-b^2/(sin(b))^2)
+end
+
+
+#### Evaluation
+function pdf(d::LogLogistic, x::Real)
+    if x ≤ zero(0)
+        z = zero(x)
+    else
+        # use built-in impletation to evaluate the density 
+        # of loglogistic at x 
+        # Y = log(X)
+        # Y ~ logistic(log(θ), 1/ϕ)
+        z = pdf(Logistic(log(d.θ), 1/d.ϕ), log(x)) / x
+    end    
+    return z
+end
+
+function logpdf(d::LogLogistic, x::Real)
+    if x ≤ zero(0)
+        z = log(zero(x))
+    else
+        z = logpdf(Logistic(log(d.θ), 1/d.ϕ), log(x)) + log(x)
+    end
+    return z 
+end
+
+function cdf(d::LogLogistic, x::Real)
+    if x <= 0
+        return 0.0
+    end 
+    z = cdf(Logistic(log(d.θ), 1/d.ϕ), log(x)) 
+    return z
+end
+
+function logcdf(d::LogLogistic, x::Real)
+    if x <= 0
+        -Inf
+    end
+    z = logcdf(Logistic(log(d.θ), 1/d.ϕ), log(x)) 
+	return z
+end
+
+function ccdf(d::LogLogistic, x::Real)
+    if x <= 0
+        return 1
+    end 
+    z = ccdf(Logistic(log(d.θ), 1/d.ϕ), log(x)) 
+	return z 
+end
+
+function logccdf(d::LogLogistic, x::Real)
+    if x <= 0
+        return 0.0
+    end
+    z = logccdf(Logistic(log(d.θ), 1/d.ϕ), log(x)) 
+	return z 
+end
+
+
+#### Sampling
+function rand(rng::AbstractRNG, d::LogLogistic)
+    u = rand(rng)
+    r = u / (1 - u)
+    return r^(1/d.ϕ)*d.θ
+end
diff --git a/src/univariates.jl b/src/univariates.jl
index 0e2ae05e32..5a5299c209 100644
--- a/src/univariates.jl
+++ b/src/univariates.jl
@@ -697,6 +697,7 @@ const continuous_distributions = [
     "levy",
     "lindley",
     "logistic",
+    "loglogistic",
     "noncentralbeta",
     "noncentralchisq",
     "noncentralf",
diff --git a/test/runtests.jl b/test/runtests.jl
index cb724278b4..236438c387 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -11,6 +11,7 @@ import JSON
 import ForwardDiff
 
 const tests = [
+    "univariate/continuous/loglogistic",
     "univariate/continuous/loguniform",
     "univariate/continuous/arcsine",
     "univariate/discrete/dirac",
@@ -77,6 +78,7 @@ const tests = [
     "univariate/continuous/gumbel",
     "univariate/continuous/lindley",
     "univariate/continuous/logistic",
+    # "univariate/continuous/loglogistic",
     "univariate/continuous/johnsonsu",
     "univariate/continuous/noncentralchisq",
     "univariate/continuous/weibull",
diff --git a/test/univariate/continuous/loglogistic.jl b/test/univariate/continuous/loglogistic.jl
new file mode 100644
index 0000000000..1aa89efbb9
--- /dev/null
+++ b/test/univariate/continuous/loglogistic.jl
@@ -0,0 +1,25 @@
+using Distributions
+using Test
+
+@testset "LogLogistic" begin 
+
+    @test round(pdf(LogLogistic(), -1), digits=6) == 0.0
+    @test round(pdf(LogLogistic(), 1), digits=6) == 0.25
+    @test round(pdf(LogLogistic(2), 2), digits=6) == 0.125
+    @test round(pdf(LogLogistic(2,2), 1), digits=6) == 0.32
+
+    @test round(cdf(LogLogistic(), -1), digits=6) == 0.0
+    @test round(cdf(LogLogistic(), 1), digits=6) == 0.5
+    @test round(cdf(LogLogistic(2), 3), digits=6) == 0.6
+    @test round(cdf(LogLogistic(2,2), 4), digits=6) == 0.8
+
+    @test round(ccdf(LogLogistic(2), 3), digits=6) == 0.4
+    @test round(ccdf(LogLogistic(2,2), 4), digits=6) == 0.2
+
+    @test round(logpdf(LogLogistic(), -1), digits=6) == -Inf
+    @test round(logpdf(LogLogistic(), 1), digits=6) == -1.386294
+
+    @test round(logcdf(LogLogistic(2,2), 4), digits=6) == -0.223144
+    @test round(logccdf(LogLogistic(2,2), 4), digits=6) == -1.609438 
+
+end
\ No newline at end of file

From bf205c5c93333a4b930da34a025e5008bcfb306e Mon Sep 17 00:00:00 2001
From: Jack Li <yli566@ucsc.edu>
Date: Tue, 10 Oct 2023 15:11:29 -0700
Subject: [PATCH 02/13] resolve issues

---
 src/univariate/continuous/loglogistic.jl | 131 +++++++++--------------
 1 file changed, 50 insertions(+), 81 deletions(-)

diff --git a/src/univariate/continuous/loglogistic.jl b/src/univariate/continuous/loglogistic.jl
index 806ede8808..557e3194ab 100644
--- a/src/univariate/continuous/loglogistic.jl
+++ b/src/univariate/continuous/loglogistic.jl
@@ -1,136 +1,105 @@
 """
-    LogLogistic(θ, ϕ)
+    LogLogistic(α, β)
 
-The *log logistic distribution* with scale `θ` and shape `ϕ` is the distribution of a random variable whose logarithm has a [`Logistic`](@ref) distribution. 
-If ``X \\sim \\operatorname{Logistic}(\\theta, \\phi)`` then ``exp(X) \\sim \\operatorname{LogLogistic}(\\theta, \\phi)``. The probability density function is 
+The *log logistic distribution* with scale `α` and shape `β` is the distribution of a random variable whose logarithm has a [`Logistic`](@ref) distribution. 
+If ``X \\sim \\operatorname{LogLogistic}(\\alpha, \\beta)`` then ``log(X) \\sim \\operatorname{Logistic}(log(\\alpha), 1/\\beta)``. The probability density function is 
 
 ```math
-f(x; \\theta, \\phi) = \\frac{(\\phi / \\theta)x/\\theta()^(\\phi - 1)}{(1 + (x/\\theta)^\\phi)^2}, \\theta > 0, \\phi > 0
+f(x; \\alpha, \\beta) = \\frac{(\\alpha / \\beta)x/\\beta()^(\\alpha - 1)}{(1 + (x/\\beta)^\\alpha)^2}, \\beta > 0, \\alpha > 0
 ```
 
 ```julia
 LogLogistic()            # Log-logistic distribution with unit scale and unit shape
-LogLogistic(θ)           # Log-logistic distribution with scale θ and unit shape
-LogLogistic(θ,ϕ)         # Log-logistic distribution with scale θ and shape ϕ
+LogLogistic(α,β)         # Log-logistic distribution with scale α and shape β
 
-params(d)                # Get the parameters, i.e. (θ, ϕ)
-scale(d)                 # Get the scale parameter, i.e. θ
-shape(d)                 # Get the shape parameter, i.e. ϕ
+params(d)                # Get the parameters, i.e. (α, β)
+scale(d)                 # Get the scale parameter, i.e. α
+shape(d)                 # Get the shape parameter, i.e. β
 ```
 
 External links
 
 * [Log logistic distribution on Wikipedia](https://en.wikipedia.org/wiki/Log-logistic_distribution)
-
 """
 
-
 struct LogLogistic{T<:Real} <: ContinuousUnivariateDistribution
-    θ::T
-    ϕ::T
-    LogLogistic{T}(θ::T,ϕ::T) where {T} = new{T}(θ,ϕ)
+    α::T
+    β::T
+    LogLogistic{T}(α::T,β::T) where {T} = new{T}(α,β)
 end
 
-function LogLogistic(θ::T, ϕ::T; check_args=true) where {T <: Real}
-    check_args && @check_args(LogLogistic, θ > zero(θ) && ϕ > zero(ϕ))
-    return LogLogistic{T}(θ, ϕ)
+function LogLogistic(α::T, β::T; check_args=true) where {T <: Real}
+    check_args && @check_args(LogLogistic, α > zero(α) && β > zero(β))
+    return LogLogistic{T}(α, β)
 end
 
-LogLogistic(θ::Real, ϕ::Real) = LogLogistic(promote(θ,ϕ)...)
-LogLogistic(θ::Integer, ϕ::Integer) = LogLogistic(float(θ), float(ϕ))
-LogLogistic(θ::T) where {T<:Real} = LogLogistic(θ, 1.0)
+LogLogistic(α::Real, β::Real) = LogLogistic(promote(α,β)...)
+LogLogistic(α::Integer, β::Integer) = LogLogistic(float(α), float(β))
 LogLogistic() = LogLogistic(1.0, 1.0, check_args=false) 
 
 @distr_support LogLogistic 0.0 Inf
 
 #### Coversions
-convert(::Type{LogLogistic{T}}, θ::S, ϕ::S) where {T <: Real, S <: Real} = LogLogistic(T(θ), T(ϕ))
-convert(::Type{LogLogistic{T}}, d::LogLogistic{S}) where {T <: Real, S <: Real} = LogLogistic(T(d.θ), T(d.ϕ), check_args=false)
-
+convert(::Type{LogLogistic{T}}, d::LogLogistic{T}) where {T<:Real} = d
+convert(::Type{LogLogistic{T}}, d::LogLogistic) where {T<:Real} = LogLogistic{T}(T(d.α), T(d.β))
 #### Parameters 
 
-params(d::LogLogistic) = (d.θ, d.ϕ)
+params(d::LogLogistic) = (d.α, d.β)
 partype(::LogLogistic{T}) where {T} = T
 
 #### Statistics 
 
-median(d::LogLogistic) = d.θ
-function mean(d::LogLogistic)
-	if d.ϕ ≤ 1
-        error("mean is defined only when ϕ > 1") 	
+median(d::LogLogistic) = d.α
+function mean(d::LogLogistic{T}) where T<:Real
+	if d.β ≤ 1
+        ArgumentError("mean is defined only when β > 1") 	
 	end
-	return d.θ*π/d.ϕ/sin(π/d.ϕ)
+	return d.α*π/d.β/sin(π/d.β)
 end
 
-function mode(d::LogLogistic)
-	if d.ϕ ≤ 1
-		error("mode is defined only when ϕ > 1")
+function mode(d::LogLogistic{T}) where T<:Real
+	if d.β ≤ 1
+		ArgumentError("mode is defined only when β > 1")
 	end 
-	return d.θ*((d.ϕ-1)/(d.ϕ+1))^(1/d.ϕ)
+	return d.α*((d.β-1)/(d.β+1))^(1/d.β)
 end
 
-function var(d::LogLogistic)
-	if d.ϕ ≤ 2
-		erros("var is defined only when ϕ > 2") 
+function var(d::LogLogistic{T}) where T<:Real
+	if d.β ≤ 2
+		ArgumentError("var is defined only when β > 2") 
 	end
-    b = π/d.ϕ
-	return d.θ^2 * (2*b/sin(2*b)-b^2/(sin(b))^2)
+    b = π/d.β
+	return d.α^2 * (2*b/sin(2*b)-b^2/(sin(b))^2)
 end
 
 
 #### Evaluation
-function pdf(d::LogLogistic, x::Real)
-    if x ≤ zero(0)
-        z = zero(x)
-    else
-        # use built-in impletation to evaluate the density 
-        # of loglogistic at x 
-        # Y = log(X)
-        # Y ~ logistic(log(θ), 1/ϕ)
-        z = pdf(Logistic(log(d.θ), 1/d.ϕ), log(x)) / x
-    end    
-    return z
+function pdf(d::LogLogistic{T}, x::Real) where T<:Real
+    # use built-in impletation to evaluate the density 
+    # of loglogistic at x 
+    # Y = log(X)
+    # Y ~ logistic(log(θ), 1/ϕ)
+    x >= 0 ? pdf(Logistic(log(d.α), 1/d.β), log(x)) / x : zero(T)
 end
 
-function logpdf(d::LogLogistic, x::Real)
-    if x ≤ zero(0)
-        z = log(zero(x))
-    else
-        z = logpdf(Logistic(log(d.θ), 1/d.ϕ), log(x)) + log(x)
-    end
-    return z 
+function logpdf(d::LogLogistic{T}, x::Real) where T<:Real
+    x >= 0 ? logpdf(Logistic(log(d.α), 1/d.β), log(x)) + log(x) : -T(Inf)
 end
 
-function cdf(d::LogLogistic, x::Real)
-    if x <= 0
-        return 0.0
-    end 
-    z = cdf(Logistic(log(d.θ), 1/d.ϕ), log(x)) 
-    return z
+function cdf(d::LogLogistic{T}, x::Real) where T<:Real
+    x >= 0 ? cdf(Logistic(log(d.α), 1/d.β), log(x)) : zero(T)
 end
 
-function logcdf(d::LogLogistic, x::Real)
-    if x <= 0
-        -Inf
-    end
-    z = logcdf(Logistic(log(d.θ), 1/d.ϕ), log(x)) 
-	return z
+function logcdf(d::LogLogistic{T}, x::Real) where T<:Real
+    x >= 0 ? logcdf(Logistic(log(d.α), 1/d.β), log(x)) : -T(Inf)
 end
 
-function ccdf(d::LogLogistic, x::Real)
-    if x <= 0
-        return 1
-    end 
-    z = ccdf(Logistic(log(d.θ), 1/d.ϕ), log(x)) 
-	return z 
+function ccdf(d::LogLogistic{T}, x::Real) where T<:Real
+    x >= 0 ? ccdf(Logistic(log(d.α), 1/d.β), log(x)) : one(T)
 end
 
-function logccdf(d::LogLogistic, x::Real)
-    if x <= 0
-        return 0.0
-    end
-    z = logccdf(Logistic(log(d.θ), 1/d.ϕ), log(x)) 
-	return z 
+function logccdf(d::LogLogistic{T}, x::Real) where T<:Real
+    x >= 0 ? logccdf(Logistic(log(d.α), 1/d.β), log(x)) : zero(T)
 end
 
 
@@ -138,5 +107,5 @@ end
 function rand(rng::AbstractRNG, d::LogLogistic)
     u = rand(rng)
     r = u / (1 - u)
-    return r^(1/d.ϕ)*d.θ
+    return r^(1/d.β)*d.α
 end

From bcc781993046d08003eaabd29d5dc24ceb501534 Mon Sep 17 00:00:00 2001
From: Jack Li <yli566@ucsc.edu>
Date: Tue, 10 Oct 2023 15:31:25 -0700
Subject: [PATCH 03/13] using sinc

---
 src/univariate/continuous/loglogistic.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/univariate/continuous/loglogistic.jl b/src/univariate/continuous/loglogistic.jl
index 557e3194ab..41e982c713 100644
--- a/src/univariate/continuous/loglogistic.jl
+++ b/src/univariate/continuous/loglogistic.jl
@@ -54,7 +54,7 @@ function mean(d::LogLogistic{T}) where T<:Real
 	if d.β ≤ 1
         ArgumentError("mean is defined only when β > 1") 	
 	end
-	return d.α*π/d.β/sin(π/d.β)
+    return d.α/sinc(1/d.β)
 end
 
 function mode(d::LogLogistic{T}) where T<:Real

From 025c8a8a1825a97f60f0abb1fa145bf234c8fd2e Mon Sep 17 00:00:00 2001
From: Jack Li <yli566@ucsc.edu>
Date: Wed, 18 Oct 2023 21:16:11 -0700
Subject: [PATCH 04/13] remove tests with a single argument

---
 test/univariate/continuous/loglogistic.jl | 3 ---
 1 file changed, 3 deletions(-)

diff --git a/test/univariate/continuous/loglogistic.jl b/test/univariate/continuous/loglogistic.jl
index 1aa89efbb9..962b0e830e 100644
--- a/test/univariate/continuous/loglogistic.jl
+++ b/test/univariate/continuous/loglogistic.jl
@@ -5,15 +5,12 @@ using Test
 
     @test round(pdf(LogLogistic(), -1), digits=6) == 0.0
     @test round(pdf(LogLogistic(), 1), digits=6) == 0.25
-    @test round(pdf(LogLogistic(2), 2), digits=6) == 0.125
     @test round(pdf(LogLogistic(2,2), 1), digits=6) == 0.32
 
     @test round(cdf(LogLogistic(), -1), digits=6) == 0.0
     @test round(cdf(LogLogistic(), 1), digits=6) == 0.5
-    @test round(cdf(LogLogistic(2), 3), digits=6) == 0.6
     @test round(cdf(LogLogistic(2,2), 4), digits=6) == 0.8
 
-    @test round(ccdf(LogLogistic(2), 3), digits=6) == 0.4
     @test round(ccdf(LogLogistic(2,2), 4), digits=6) == 0.2
 
     @test round(logpdf(LogLogistic(), -1), digits=6) == -Inf

From c82b8b8e32a2406f25af09f953e7093d3fd289e7 Mon Sep 17 00:00:00 2001
From: David Widmann <devmotion@users.noreply.github.com>
Date: Fri, 17 Oct 2025 05:30:45 -0600
Subject: [PATCH 05/13] Fix docs

---
 docs/Project.toml      | 3 +++
 docs/src/univariate.md | 8 ++++----
 2 files changed, 7 insertions(+), 4 deletions(-)

diff --git a/docs/Project.toml b/docs/Project.toml
index c7a818b0ba..9d866dbf41 100644
--- a/docs/Project.toml
+++ b/docs/Project.toml
@@ -6,3 +6,6 @@ GR = "28b8d3ca-fb5f-59d9-8090-bfdbd6d07a71"
 [compat]
 Documenter = "1"
 GR = "0.72.1, 0.73"
+
+[sources.Distributions]
+path = ".."
diff --git a/docs/src/univariate.md b/docs/src/univariate.md
index 78ed16d4a2..ed6b1c9484 100644
--- a/docs/src/univariate.md
+++ b/docs/src/univariate.md
@@ -320,17 +320,17 @@ plotdensity((0, 20), Lindley, (1.5,)) # hide
 ```
 
 ```@docs
-logistic
+Logistic
 ```
 ```@example plotdensity
-plotdensity((-4, 8), logistic, (2, 1)) # hide
+plotdensity((-4, 8), Logistic, (2, 1)) # hide
 ```
 
 ```@docs
-loglogistic
+LogLogistic
 ```
 ```@example plotdensity
-plotdensity((0, 2), logistic, (1, 1)) # hide
+plotdensity((0, 2), LogLogistic, (1, 1)) # hide
 ```
 
 ```@docs

From 4afe62616e13db6823ddd392df46e0ce5c223679 Mon Sep 17 00:00:00 2001
From: David Widmann <devmotion@users.noreply.github.com>
Date: Fri, 17 Oct 2025 05:31:07 -0600
Subject: [PATCH 06/13] Simplify test/runtests.jl diff

---
 test/runtests.jl | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/test/runtests.jl b/test/runtests.jl
index 72282890bd..39b5e65aac 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -12,7 +12,6 @@ import ForwardDiff
 
 const tests = [
     "aqua",
-    "univariate/continuous/loglogistic",
     "univariate/continuous/loguniform",
     "univariate/continuous/arcsine",
     "univariate/discrete/dirac",
@@ -82,7 +81,7 @@ const tests = [
     "univariate/continuous/gumbel",
     "univariate/continuous/lindley",
     "univariate/continuous/logistic",
-    # "univariate/continuous/loglogistic",
+    "univariate/continuous/loglogistic",
     "univariate/continuous/johnsonsu",
     "univariate/continuous/noncentralchisq",
     "univariate/continuous/weibull",

From 28d0b37a8534c6506fcbdc80f0543dd246d56043 Mon Sep 17 00:00:00 2001
From: David Widmann <devmotion@users.noreply.github.com>
Date: Fri, 17 Oct 2025 17:59:01 -0600
Subject: [PATCH 07/13] Fixes

---
 src/univariate/continuous/loglogistic.jl | 90 +++++++++++++-----------
 test/ref/continuous/loglogistic.R        | 38 ++++++++++
 test/ref/readme.md                       |  2 +-
 3 files changed, 89 insertions(+), 41 deletions(-)
 create mode 100644 test/ref/continuous/loglogistic.R

diff --git a/src/univariate/continuous/loglogistic.jl b/src/univariate/continuous/loglogistic.jl
index 41e982c713..952fc069d7 100644
--- a/src/univariate/continuous/loglogistic.jl
+++ b/src/univariate/continuous/loglogistic.jl
@@ -1,7 +1,7 @@
 """
     LogLogistic(α, β)
 
-The *log logistic distribution* with scale `α` and shape `β` is the distribution of a random variable whose logarithm has a [`Logistic`](@ref) distribution. 
+The *log-logistic distribution* with scale `α` and shape `β` is the distribution of a random variable whose logarithm has a [`Logistic`](@ref) distribution. 
 If ``X \\sim \\operatorname{LogLogistic}(\\alpha, \\beta)`` then ``log(X) \\sim \\operatorname{Logistic}(log(\\alpha), 1/\\beta)``. The probability density function is 
 
 ```math
@@ -21,7 +21,6 @@ External links
 
 * [Log logistic distribution on Wikipedia](https://en.wikipedia.org/wiki/Log-logistic_distribution)
 """
-
 struct LogLogistic{T<:Real} <: ContinuousUnivariateDistribution
     α::T
     β::T
@@ -42,70 +41,81 @@ LogLogistic() = LogLogistic(1.0, 1.0, check_args=false)
 #### Coversions
 convert(::Type{LogLogistic{T}}, d::LogLogistic{T}) where {T<:Real} = d
 convert(::Type{LogLogistic{T}}, d::LogLogistic) where {T<:Real} = LogLogistic{T}(T(d.α), T(d.β))
-#### Parameters 
 
+#### Parameters
 params(d::LogLogistic) = (d.α, d.β)
 partype(::LogLogistic{T}) where {T} = T
 
 #### Statistics 
 
 median(d::LogLogistic) = d.α
-function mean(d::LogLogistic{T}) where T<:Real
-	if d.β ≤ 1
-        ArgumentError("mean is defined only when β > 1") 	
+function mean(d::LogLogistic)
+    (; α, β) = d
+	if !(β > 1)
+        ArgumentError("the mean of a log-logistic distribution is defined only when its shape β > 1") 	
 	end
-    return d.α/sinc(1/d.β)
+    return α/sinc(inv(β))
 end
 
-function mode(d::LogLogistic{T}) where T<:Real
-	if d.β ≤ 1
-		ArgumentError("mode is defined only when β > 1")
-	end 
-	return d.α*((d.β-1)/(d.β+1))^(1/d.β)
+function mode(d::LogLogistic)
+    (; α, β) = d
+    return α*(max(β - 1, 0) / (β + 1))^inv(β)
 end
 
-function var(d::LogLogistic{T}) where T<:Real
-	if d.β ≤ 2
-		ArgumentError("var is defined only when β > 2") 
+function var(d::LogLogistic)
+    (; α, β) = d
+	if !(β > 2)
+        ArgumentError("the variance of a log-logistic distribution is defined only when its shape β > 2") 	
 	end
-    b = π/d.β
-	return d.α^2 * (2*b/sin(2*b)-b^2/(sin(b))^2)
+    invβ = inv(β)
+	return α^2 * (inv(sinc(2 * invβ)) - inv(sinc(invβ))^2)
 end
 
+entropy(d::LogLogistic) = log(d.α / d.β) + 2
 
 #### Evaluation
-function pdf(d::LogLogistic{T}, x::Real) where T<:Real
-    # use built-in impletation to evaluate the density 
-    # of loglogistic at x 
-    # Y = log(X)
-    # Y ~ logistic(log(θ), 1/ϕ)
-    x >= 0 ? pdf(Logistic(log(d.α), 1/d.β), log(x)) / x : zero(T)
-end
 
-function logpdf(d::LogLogistic{T}, x::Real) where T<:Real
-    x >= 0 ? logpdf(Logistic(log(d.α), 1/d.β), log(x)) + log(x) : -T(Inf)
+function pdf(d::LogLogistic, x::Real)
+    (; α, β) = d
+    insupport = x > 0
+    _x = insupport ? x : zero(x)
+    xoαβ = (_x / α)^β
+    res = (β / x) / ((1 + xoαβ) * (1 + inv(xoαβ)))
+    return insupport ? res : zero(res)
 end
-
-function cdf(d::LogLogistic{T}, x::Real) where T<:Real
-    x >= 0 ? cdf(Logistic(log(d.α), 1/d.β), log(x)) : zero(T)
+function logpdf(d::LogLogistic, x::Real)
+    (; α, β) = d
+    insupport = x > 0
+    _x = insupport ? x : zero(x)
+    βlogxoα = β * log(_x / α)
+    res = log(β / x) - (log1pexp(βlogxoα) + log1pexp(-βlogxoα))
+    return insupport ? res : oftype(res, -Inf)
 end
 
-function logcdf(d::LogLogistic{T}, x::Real) where T<:Real
-    x >= 0 ? logcdf(Logistic(log(d.α), 1/d.β), log(x)) : -T(Inf)
-end
+cdf(d::LogLogistic, x::Real) = inv(1 + (max(x, 0) / d.α)^(-d.β))
+ccdf(d::LogLogistic, x::Real) = inv(1 + (max(x, 0) / d.α)^d.β)
 
-function ccdf(d::LogLogistic{T}, x::Real) where T<:Real
-    x >= 0 ? ccdf(Logistic(log(d.α), 1/d.β), log(x)) : one(T)
-end
+logcdf(d::LogLogistic, x::Real) = -log1pexp(-d.β * log(max(x, 0) / d.α))
+logccdf(d::LogLogistic, x::Real) = -log1pexp(d.β * log(max(x, 0) / d.α))
 
-function logccdf(d::LogLogistic{T}, x::Real) where T<:Real
-    x >= 0 ? logccdf(Logistic(log(d.α), 1/d.β), log(x)) : zero(T)
-end
+quantile(d::LogLogistic, p::Real) = d.α * (p / (1 - p))^inv(d.β)
+cquantile(d::LogLogistic, p::Real) = d.α * ((1 - p) / p)^inv(d.β)
 
+invlogcdf(d::LogLogistic, lp::Real) = d.α * expm1(-lp)^(-inv(d.β))
+invlogccdf(d::LogLogistic, lp::Real) = d.α * expm1(-lp)^inv(d.β)
 
 #### Sampling
+
 function rand(rng::AbstractRNG, d::LogLogistic)
     u = rand(rng)
-    r = u / (1 - u)
-    return r^(1/d.β)*d.α
+    return d.α * (u / (1 - u))^(inv(d.β))
+end
+function rand!(rng::AbstractRNG, d::LogLogistic, A::AbstractArray{<:Real})
+    rand!(rng, A)
+    let α = d.α, invβ = inv(d.β)
+        map!(A, A) do u
+            return α * (u / (1 - u))^invβ
+        end
+    end
+    return A
 end
diff --git a/test/ref/continuous/loglogistic.R b/test/ref/continuous/loglogistic.R
new file mode 100644
index 0000000000..f405386f02
--- /dev/null
+++ b/test/ref/continuous/loglogistic.R
@@ -0,0 +1,38 @@
+LogLogistic <- R6Class("LogLogistic",
+    inherit = ContinuousDistribution,
+    public = list(
+        names = c("alpha", "beta"),
+        alpha = NA,
+        beta = NA,
+        initialize = function(a=1, b=1) {
+            self$alpha <- a
+            self$beta <- b
+        },
+        supp = function() { c(0, Inf) },
+        properties = function() {
+            a <- self$alpha
+            b <- self$beta
+            g1 <- ifelse(a > 1, gamma(1 - 1/a), NaN)
+            g2 <- ifelse(a > 2, gamma(1 - 2/a), NaN)
+            g3 <- ifelse(a > 3, gamma(1 - 3/a), NaN)
+            g4 <- ifelse(a > 4, gamma(1 - 4/a), NaN)
+            gam <- 0.57721566490153286
+            list(shape = a,
+                 scale = b,
+                 mean = ifelse(b > 1, a, NaN),
+                 median = a,
+                 mode = ifelse(b > 1, b * (a / (1 + a))^(1/a), 0.0),
+                 var = ifelse(a > 2, b^2 * (g2 - g1^2), NaN),
+                 skewness = if (a > 3) {
+                     (g3 - 3 * g2 * g1 + 2 * g1^3) / (g2 - g1^2)^1.5
+                 } else { Inf },
+                 kurtosis = if (a > 4) {
+                     (g4 - 4 * g3 * g1 + 3 * g2^2) / (g2 - g1^2)^2 - 6
+                 } else { Inf },
+                 entropy = 2 + log(a / b))
+        },
+        pdf = function(x, log=FALSE) { VGAM::dfisk(x, shape=self$alpha, scale=self$beta, log=log) },
+        cdf = function(x) { VGAM::pfisk(x, shape=self$alpha, scale=self$beta) },
+        quan = function(v) { VGAM::qfisk(v, shape=self$alpha, scale=self$beta) }
+    )
+)
diff --git a/test/ref/readme.md b/test/ref/readme.md
index 7ae82d5d2e..3568ef0b7b 100644
--- a/test/ref/readme.md
+++ b/test/ref/readme.md
@@ -15,7 +15,7 @@ in addition to the R language itself:
 | stringr     | For string parsing  |
 | R6          | OOP for implementing distributions |
 | extraDistr  | A number of distributions |
-| VGAM        | For ``Frechet`` and ``Levy`` |
+| VGAM        | For ``LogLogistic``, ``Frechet`` and ``Levy`` |
 | distr       | For ``Arcsine`` |
 | chi         | For ``Chi`` |
 | circular    | For ``VonMises`` |

From 864a4981209c22d69859779415b81270ac90cf41 Mon Sep 17 00:00:00 2001
From: David Widmann <devmotion@users.noreply.github.com>
Date: Sun, 26 Oct 2025 23:43:15 +0100
Subject: [PATCH 08/13] More tests

---
 src/univariate/continuous/loglogistic.jl  |  9 +--
 test/univariate/continuous/loglogistic.jl | 68 ++++++++++++++++++-----
 2 files changed, 58 insertions(+), 19 deletions(-)

diff --git a/src/univariate/continuous/loglogistic.jl b/src/univariate/continuous/loglogistic.jl
index 952fc069d7..31957a2c32 100644
--- a/src/univariate/continuous/loglogistic.jl
+++ b/src/univariate/continuous/loglogistic.jl
@@ -9,8 +9,7 @@ f(x; \\alpha, \\beta) = \\frac{(\\alpha / \\beta)x/\\beta()^(\\alpha - 1)}{(1 +
 ```
 
 ```julia
-LogLogistic()            # Log-logistic distribution with unit scale and unit shape
-LogLogistic(α,β)         # Log-logistic distribution with scale α and shape β
+LogLogistic(α, β)        # Log-logistic distribution with scale α and shape β
 
 params(d)                # Get the parameters, i.e. (α, β)
 scale(d)                 # Get the scale parameter, i.e. α
@@ -32,9 +31,7 @@ function LogLogistic(α::T, β::T; check_args=true) where {T <: Real}
     return LogLogistic{T}(α, β)
 end
 
-LogLogistic(α::Real, β::Real) = LogLogistic(promote(α,β)...)
-LogLogistic(α::Integer, β::Integer) = LogLogistic(float(α), float(β))
-LogLogistic() = LogLogistic(1.0, 1.0, check_args=false) 
+LogLogistic(α::Real, β::Real) = LogLogistic(promote(α, β)...)
 
 @distr_support LogLogistic 0.0 Inf
 
@@ -88,7 +85,7 @@ function logpdf(d::LogLogistic, x::Real)
     insupport = x > 0
     _x = insupport ? x : zero(x)
     βlogxoα = β * log(_x / α)
-    res = log(β / x) - (log1pexp(βlogxoα) + log1pexp(-βlogxoα))
+    res = log(β / _x) - (log1pexp(βlogxoα) + log1pexp(-βlogxoα))
     return insupport ? res : oftype(res, -Inf)
 end
 
diff --git a/test/univariate/continuous/loglogistic.jl b/test/univariate/continuous/loglogistic.jl
index 962b0e830e..2c1b354151 100644
--- a/test/univariate/continuous/loglogistic.jl
+++ b/test/univariate/continuous/loglogistic.jl
@@ -1,22 +1,64 @@
 using Distributions
 using Test
 
-@testset "LogLogistic" begin 
+@testset "LogLogistic" begin
+    @testset "Conversion" begin
+        d = LogLogistic(1.0, 2.0)
+        @test convert(LogLogistic{Float64}, d) === d
+        @test convert(LogLogistic{Float32}, d) isa LogLogistic{Float32}
+        @test convert(LogLogistic{Float32}, d) == d
+    end
 
-    @test round(pdf(LogLogistic(), -1), digits=6) == 0.0
-    @test round(pdf(LogLogistic(), 1), digits=6) == 0.25
-    @test round(pdf(LogLogistic(2,2), 1), digits=6) == 0.32
+    # Values computed with WolframAlpha
+    @testset "Special values" begin
+        # pdf
+        @test iszero(pdf(LogLogistic(1, 1), -1))
+        @test pdf(LogLogistic(1, 1), 1) ≈ 0.25
+        @test pdf(LogLogistic(2, 2), 1) ≈ 0.32
+        @test pdf(LogLogistic(2, 2), 4) ≈ 0.08
 
-    @test round(cdf(LogLogistic(), -1), digits=6) == 0.0
-    @test round(cdf(LogLogistic(), 1), digits=6) == 0.5
-    @test round(cdf(LogLogistic(2,2), 4), digits=6) == 0.8
+        # log pdf
+        @test logpdf(LogLogistic(1, 1), -1) == -Inf
+        @test logpdf(LogLogistic(1, 1), 1) ≈ -log(4)
+        @test logpdf(LogLogistic(2, 2), 1) ≈ log(0.32)
+        @test logpdf(LogLogistic(2, 2), 4) ≈ log(0.08)
 
-    @test round(ccdf(LogLogistic(2,2), 4), digits=6) == 0.2
+        # cdf
+        @test iszero(cdf(LogLogistic(1, 1), -1))
+        @test cdf(LogLogistic(1, 1), Inf) == 1
+        @test cdf(LogLogistic(1, 1), 1) ≈ 0.5
+        @test cdf(LogLogistic(2, 2), 1) ≈ 0.2
+        @test cdf(LogLogistic(2, 2), 4) ≈ 0.8
 
-    @test round(logpdf(LogLogistic(), -1), digits=6) == -Inf
-    @test round(logpdf(LogLogistic(), 1), digits=6) == -1.386294
+        # log cdf
+        @test logcdf(LogLogistic(1, 1), -1) == -Inf
+        @test iszero(logcdf(LogLogistic(1, 1), Inf))
+        @test logcdf(LogLogistic(1, 1), 1) ≈ -log(2)
+        @test logcdf(LogLogistic(2, 2), 1) ≈ log(0.2)
+        @test logcdf(LogLogistic(2, 2), 4) ≈ log(0.8)
 
-    @test round(logcdf(LogLogistic(2,2), 4), digits=6) == -0.223144
-    @test round(logccdf(LogLogistic(2,2), 4), digits=6) == -1.609438 
+        # ccdf
+        @test ccdf(LogLogistic(1, 1), -1) == 1
+        @test iszero(ccdf(LogLogistic(1, 1), Inf))
+        @test ccdf(LogLogistic(1, 1), 1) ≈ 0.5
+        @test ccdf(LogLogistic(2, 2), 1) ≈ 0.8
+        @test ccdf(LogLogistic(2, 2), 4) ≈ 0.2
 
-end
\ No newline at end of file
+        # log ccdf
+        @test iszero(logccdf(LogLogistic(1, 1), -1))
+        @test logccdf(LogLogistic(1, 1), Inf) == -Inf
+        @test logccdf(LogLogistic(1, 1), 1) ≈ -log(2)
+        @test logccdf(LogLogistic(2, 2), 1) ≈ log(0.8)
+        @test logccdf(LogLogistic(2, 2), 4) ≈ log(0.2)
+    end
+
+    @testset "Default tests" begin
+        for d in [
+            LogLogistic(1, 1),
+            LogLogistic(2, 1),
+            LogLogistic(2, 2),
+        ]
+            test_distr(d, 10^6)
+        end
+    end
+end

From 6b2e02c2b333f8f09c2055df197cb5d1027e4b1c Mon Sep 17 00:00:00 2001
From: David Widmann <devmotion@users.noreply.github.com>
Date: Mon, 27 Oct 2025 14:49:57 +0100
Subject: [PATCH 09/13] More fixes and tests

---
 Project.toml                              |  4 +-
 src/univariate/continuous/loglogistic.jl  | 10 ++--
 test/testutils.jl                         |  1 +
 test/univariate/continuous/loglogistic.jl | 70 +++++++++++++++++++++++
 4 files changed, 79 insertions(+), 6 deletions(-)

diff --git a/Project.toml b/Project.toml
index 643ea0f47e..ed35734f8f 100644
--- a/Project.toml
+++ b/Project.toml
@@ -43,6 +43,7 @@ FiniteDifferences = "0.12"
 ForwardDiff = "0.10, 1"
 JSON = "0.21"
 LinearAlgebra = "<0.0.1, 1"
+Optim = "1.13"
 OffsetArrays = "1"
 PDMats = "0.11.35"
 Printf = "<0.0.1, 1"
@@ -69,6 +70,7 @@ Distributed = "8ba89e20-285c-5b6f-9357-94700520ee1b"
 FiniteDifferences = "26cc04aa-876d-5657-8c51-4c34ba976000"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 JSON = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
+Optim = "429524aa-4258-5aef-a3af-852621145aeb"
 OffsetArrays = "6fe1bfb0-de20-5000-8ca7-80f57d26f881"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 StableRNGs = "860ef19b-820b-49d6-a774-d7a799459cd3"
@@ -76,4 +78,4 @@ StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
-test = ["Aqua", "StableRNGs", "Calculus", "ChainRulesCore", "ChainRulesTestUtils", "DensityInterface", "Distributed", "FiniteDifferences", "ForwardDiff", "JSON", "SparseArrays", "StaticArrays", "Test", "OffsetArrays"]
+test = ["Aqua", "StableRNGs", "Calculus", "ChainRulesCore", "ChainRulesTestUtils", "DensityInterface", "Distributed", "FiniteDifferences", "ForwardDiff", "JSON", "Optim", "SparseArrays", "StaticArrays", "Test", "OffsetArrays"]
diff --git a/src/univariate/continuous/loglogistic.jl b/src/univariate/continuous/loglogistic.jl
index 31957a2c32..8a5ba67b16 100644
--- a/src/univariate/continuous/loglogistic.jl
+++ b/src/univariate/continuous/loglogistic.jl
@@ -26,12 +26,12 @@ struct LogLogistic{T<:Real} <: ContinuousUnivariateDistribution
     LogLogistic{T}(α::T,β::T) where {T} = new{T}(α,β)
 end
 
-function LogLogistic(α::T, β::T; check_args=true) where {T <: Real}
+function LogLogistic(α::T, β::T; check_args::Bool=true) where {T <: Real}
     check_args && @check_args(LogLogistic, α > zero(α) && β > zero(β))
     return LogLogistic{T}(α, β)
 end
 
-LogLogistic(α::Real, β::Real) = LogLogistic(promote(α, β)...)
+LogLogistic(α::Real, β::Real; check_args::Bool = true) = LogLogistic(promote(α, β)...; check_args)
 
 @distr_support LogLogistic 0.0 Inf
 
@@ -49,7 +49,7 @@ median(d::LogLogistic) = d.α
 function mean(d::LogLogistic)
     (; α, β) = d
 	if !(β > 1)
-        ArgumentError("the mean of a log-logistic distribution is defined only when its shape β > 1") 	
+        throw(ArgumentError("the mean of a log-logistic distribution is defined only when its shape β > 1"))
 	end
     return α/sinc(inv(β))
 end
@@ -62,7 +62,7 @@ end
 function var(d::LogLogistic)
     (; α, β) = d
 	if !(β > 2)
-        ArgumentError("the variance of a log-logistic distribution is defined only when its shape β > 2") 	
+        throw(ArgumentError("the variance of a log-logistic distribution is defined only when its shape β > 2"))
 	end
     invβ = inv(β)
 	return α^2 * (inv(sinc(2 * invβ)) - inv(sinc(invβ))^2)
@@ -77,7 +77,7 @@ function pdf(d::LogLogistic, x::Real)
     insupport = x > 0
     _x = insupport ? x : zero(x)
     xoαβ = (_x / α)^β
-    res = (β / x) / ((1 + xoαβ) * (1 + inv(xoαβ)))
+    res = (β / _x) / ((1 + xoαβ) * (1 + inv(xoαβ)))
     return insupport ? res : zero(res)
 end
 function logpdf(d::LogLogistic, x::Real)
diff --git a/test/testutils.jl b/test/testutils.jl
index 46737e06d1..8a62c52d3b 100644
--- a/test/testutils.jl
+++ b/test/testutils.jl
@@ -626,6 +626,7 @@ allow_test_stats(d::UnivariateDistribution) = true
 allow_test_stats(d::NoncentralBeta) = false
 allow_test_stats(::StudentizedRange) = false
 allow_test_stats(::LogitNormal) = false # `mean` is not defined since it has no analytical solution
+allow_test_stats(d::LogLogistic) = d.β > 2 # second moment is only defined if shape β > 2
 
 function test_stats(d::ContinuousUnivariateDistribution, xs::AbstractVector{Float64})
     # using Monte Carlo methods
diff --git a/test/univariate/continuous/loglogistic.jl b/test/univariate/continuous/loglogistic.jl
index 2c1b354151..9705a7ec03 100644
--- a/test/univariate/continuous/loglogistic.jl
+++ b/test/univariate/continuous/loglogistic.jl
@@ -1,7 +1,32 @@
 using Distributions
 using Test
 
+import Optim
+
 @testset "LogLogistic" begin
+    @testset "Constructors" begin
+        for T1 in (Int, Float32, Float64), T2 in (Int, Float32, Float64)
+           d = @inferred(LogLogistic(T1(1), T2(2)))
+           @test d isa LogLogistic{promote_type(T1, T2)}
+           @test d.α == 1
+           @test d.β == 2
+
+           @test_throws ArgumentError LogLogistic(T1(-1), T2(2))
+           @test_throws ArgumentError LogLogistic(T1(-1), T2(2); check_args=true)
+           d = @inferred(LogLogistic(T1(-1), T2(2); check_args=false))
+           @test d isa LogLogistic{promote_type(T1, T2)}
+           @test d.α == -1
+           @test d.β == 2
+
+           @test_throws ArgumentError LogLogistic(T1(1), T2(-2))
+           @test_throws ArgumentError LogLogistic(T1(1), T2(-2); check_args=true)
+           d = @inferred(LogLogistic(T1(1), T2(-2); check_args=false))
+           @test d isa LogLogistic{promote_type(T1, T2)}
+           @test d.α == 1
+           @test d.β == -2
+        end
+    end
+
     @testset "Conversion" begin
         d = LogLogistic(1.0, 2.0)
         @test convert(LogLogistic{Float64}, d) === d
@@ -9,6 +34,44 @@ using Test
         @test convert(LogLogistic{Float32}, d) == d
     end
 
+    @testset "median" begin
+        for α in (0.5, 1, 2, 3), β in (0.5, 1, 2, 3)
+            d = LogLogistic(α, β)
+            @test median(d) ≈ quantile(d, 1//2)
+        end
+    end
+
+    @testset "mode" begin
+        for α in (0.5, 1, 2, 3), β in (0.5, 1, 2, 3)
+            d = LogLogistic(α, β)
+            opt = Optim.maximize(Base.Fix1(logpdf, d), 0.0, 10.0)
+            @test mode(d) ≈ Optim.maximizer(opt) rtol = 1e-8 atol = 1e-12
+        end
+    end
+
+    @testset "mean" begin
+        for α in (0.5, 1, 2, 3), β in (0.5, 1, 2, 3)
+            d = LogLogistic(α, β)
+            if β > 1
+                @test mean(d) ≈ Distributions.expectation(identity, d)
+            else
+                @test_throws ArgumentError("the mean of a log-logistic distribution is defined only when its shape β > 1") mean(d)
+            end
+        end
+    end
+
+    @testset "variance" begin
+        for α in (0.5, 1, 2, 3), β in (0.5, 1, 2, 3)
+            d = LogLogistic(α, β)
+            if β > 2
+                m = mean(d)
+                @test var(d) ≈ Distributions.expectation(x -> (x - m)^2, d)
+            else
+                @test_throws ArgumentError("the variance of a log-logistic distribution is defined only when its shape β > 2") var(d)
+            end
+        end
+    end
+
     # Values computed with WolframAlpha
     @testset "Special values" begin
         # pdf
@@ -52,6 +115,13 @@ using Test
         @test logccdf(LogLogistic(2, 2), 4) ≈ log(0.2)
     end
 
+    @testset "entropy" begin
+        for α in (0.5, 1, 2, 3), β in (0.5, 1, 2, 3)
+            d = LogLogistic(α, β)
+            @test entropy(d) ≈ -Distributions.expectation(Base.Fix1(logpdf, d), d) rtol = 1e-6
+        end
+    end
+
     @testset "Default tests" begin
         for d in [
             LogLogistic(1, 1),

From 4a5f3d57caa4bb819c4df598c654ee1219f08223 Mon Sep 17 00:00:00 2001
From: David Widmann <devmotion@users.noreply.github.com>
Date: Mon, 27 Oct 2025 16:10:16 +0100
Subject: [PATCH 10/13] More tests

---
 test/univariate/continuous/loglogistic.jl | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/test/univariate/continuous/loglogistic.jl b/test/univariate/continuous/loglogistic.jl
index 9705a7ec03..a0da9a5b23 100644
--- a/test/univariate/continuous/loglogistic.jl
+++ b/test/univariate/continuous/loglogistic.jl
@@ -8,6 +8,7 @@ import Optim
         for T1 in (Int, Float32, Float64), T2 in (Int, Float32, Float64)
            d = @inferred(LogLogistic(T1(1), T2(2)))
            @test d isa LogLogistic{promote_type(T1, T2)}
+           @test partype(d) === promote_type(T1, T2)
            @test d.α == 1
            @test d.β == 2
 
@@ -15,6 +16,7 @@ import Optim
            @test_throws ArgumentError LogLogistic(T1(-1), T2(2); check_args=true)
            d = @inferred(LogLogistic(T1(-1), T2(2); check_args=false))
            @test d isa LogLogistic{promote_type(T1, T2)}
+           @test partype(d) === promote_type(T1, T2)
            @test d.α == -1
            @test d.β == 2
 
@@ -22,6 +24,7 @@ import Optim
            @test_throws ArgumentError LogLogistic(T1(1), T2(-2); check_args=true)
            d = @inferred(LogLogistic(T1(1), T2(-2); check_args=false))
            @test d isa LogLogistic{promote_type(T1, T2)}
+           @test partype(d) === promote_type(T1, T2)
            @test d.α == 1
            @test d.β == -2
         end

From f50f5a6ccfc3c7e02044a6994121656c03fe54ef Mon Sep 17 00:00:00 2001
From: David Widmann <devmotion@users.noreply.github.com>
Date: Mon, 27 Oct 2025 17:08:19 +0100
Subject: [PATCH 11/13] Add tests against R (VGAM)

---
 test/ref/continuous/loglogistic.R |  31 +----
 test/ref/continuous_test.lst      |   8 ++
 test/ref/continuous_test.ref.json | 182 ++++++++++++++++++++++++++++++
 test/ref/rdistributions.R         |   1 +
 4 files changed, 196 insertions(+), 26 deletions(-)

diff --git a/test/ref/continuous/loglogistic.R b/test/ref/continuous/loglogistic.R
index f405386f02..6a89ea3adb 100644
--- a/test/ref/continuous/loglogistic.R
+++ b/test/ref/continuous/loglogistic.R
@@ -4,35 +4,14 @@ LogLogistic <- R6Class("LogLogistic",
         names = c("alpha", "beta"),
         alpha = NA,
         beta = NA,
-        initialize = function(a=1, b=1) {
+        initialize = function(a, b) {
             self$alpha <- a
             self$beta <- b
         },
         supp = function() { c(0, Inf) },
-        properties = function() {
-            a <- self$alpha
-            b <- self$beta
-            g1 <- ifelse(a > 1, gamma(1 - 1/a), NaN)
-            g2 <- ifelse(a > 2, gamma(1 - 2/a), NaN)
-            g3 <- ifelse(a > 3, gamma(1 - 3/a), NaN)
-            g4 <- ifelse(a > 4, gamma(1 - 4/a), NaN)
-            gam <- 0.57721566490153286
-            list(shape = a,
-                 scale = b,
-                 mean = ifelse(b > 1, a, NaN),
-                 median = a,
-                 mode = ifelse(b > 1, b * (a / (1 + a))^(1/a), 0.0),
-                 var = ifelse(a > 2, b^2 * (g2 - g1^2), NaN),
-                 skewness = if (a > 3) {
-                     (g3 - 3 * g2 * g1 + 2 * g1^3) / (g2 - g1^2)^1.5
-                 } else { Inf },
-                 kurtosis = if (a > 4) {
-                     (g4 - 4 * g3 * g1 + 3 * g2^2) / (g2 - g1^2)^2 - 6
-                 } else { Inf },
-                 entropy = 2 + log(a / b))
-        },
-        pdf = function(x, log=FALSE) { VGAM::dfisk(x, shape=self$alpha, scale=self$beta, log=log) },
-        cdf = function(x) { VGAM::pfisk(x, shape=self$alpha, scale=self$beta) },
-        quan = function(v) { VGAM::qfisk(v, shape=self$alpha, scale=self$beta) }
+        properties = function() { },
+        pdf = function(x, log=FALSE) { VGAM::dfisk(x, scale=self$alpha, shape=self$beta, log=log) },
+        cdf = function(x) { VGAM::pfisk(x, scale=self$alpha, shape=self$beta) },
+        quan = function(v) { VGAM::qfisk(v, scale=self$alpha, shape=self$beta) }
     )
 )
diff --git a/test/ref/continuous_test.lst b/test/ref/continuous_test.lst
index d403be3e65..a937ceb719 100644
--- a/test/ref/continuous_test.lst
+++ b/test/ref/continuous_test.lst
@@ -126,6 +126,14 @@ Logistic(5.0, 1.0)
 Logistic(2.0, 1.5)
 Logistic(5.0, 1.5)
 
+LogLogistic(0.5, 0.5)
+LogLogistic(0.5, 1.0)
+LogLogistic(1.0, 0.5)
+LogLogistic(1.0, 1.0)
+LogLogistic(1.0, 2.0)
+LogLogistic(2.0, 1.0)
+LogLogistic(2.0, 2.0)
+
 LogNormal()
 LogNormal(1.0)
 LogNormal(0.0, 2.0)
diff --git a/test/ref/continuous_test.ref.json b/test/ref/continuous_test.ref.json
index ae86f2e8a7..edede917a7 100644
--- a/test/ref/continuous_test.ref.json
+++ b/test/ref/continuous_test.ref.json
@@ -3457,6 +3457,188 @@
     { "q": 0.90, "x": 8.29583686600433 }
   ]
 },
+{
+  "expr": "LogLogistic(0.5, 0.5)",
+  "dtype": "LogLogistic",
+  "minimum": 0,
+  "maximum": "inf",
+  "properties": {
+  },
+  "points": [
+    { "x": 0.00617283950617284, "pdf": 7.29, "logpdf": 1.98650354602057, "cdf": 0.1 },
+    { "x": 0.03125, "pdf": 2.56, "logpdf": 0.940007258491471, "cdf": 0.2 },
+    { "x": 0.0918367346938776, "pdf": 1.14333333333333, "logpdf": 0.133947972509739, "cdf": 0.3 },
+    { "x": 0.222222222222222, "pdf": 0.54, "logpdf": -0.616186139423817, "cdf": 0.4 },
+    { "x": 0.5, "pdf": 0.25, "logpdf": -1.38629436111989, "cdf": 0.5 },
+    { "x": 1.125, "pdf": 0.106666666666667, "logpdf": -2.23804657185647, "cdf": 0.6 },
+    { "x": 2.72222222222222, "pdf": 0.0385714285714285, "logpdf": -3.25524346903908, "cdf": 0.7 },
+    { "x": 8, "pdf": 0.01, "logpdf": -4.60517018598809, "cdf": 0.8 },
+    { "x": 40.5, "pdf": 0.00111111111111111, "logpdf": -6.80239476332431, "cdf": 0.9 }
+  ],
+  "quans": [
+    { "q": 0.10, "x": 0.00617283950617284 },
+    { "q": 0.25, "x": 0.0555555555555556 },
+    { "q": 0.50, "x": 0.5 },
+    { "q": 0.75, "x": 4.5 },
+    { "q": 0.90, "x": 40.5 }
+  ]
+},
+{
+  "expr": "LogLogistic(0.5, 1.0)",
+  "dtype": "LogLogistic",
+  "minimum": 0,
+  "maximum": "inf",
+  "properties": {
+  },
+  "points": [
+    { "x": 0.0555555555555556, "pdf": 1.62, "logpdf": 0.482426149244293, "cdf": 0.1 },
+    { "x": 0.125, "pdf": 1.28, "logpdf": 0.246860077931526, "cdf": 0.2 },
+    { "x": 0.214285714285714, "pdf": 0.98, "logpdf": -0.0202027073175196, "cdf": 0.3 },
+    { "x": 0.333333333333333, "pdf": 0.72, "logpdf": -0.328504066972036, "cdf": 0.4 },
+    { "x": 0.5, "pdf": 0.5, "logpdf": -0.693147180559945, "cdf": 0.5 },
+    { "x": 0.75, "pdf": 0.32, "logpdf": -1.13943428318836, "cdf": 0.6 },
+    { "x": 1.16666666666667, "pdf": 0.18, "logpdf": -1.71479842809193, "cdf": 0.7 },
+    { "x": 2, "pdf": 0.08, "logpdf": -2.52572864430826, "cdf": 0.8 },
+    { "x": 4.5, "pdf": 0.02, "logpdf": -3.91202300542815, "cdf": 0.9 }
+  ],
+  "quans": [
+    { "q": 0.10, "x": 0.0555555555555556 },
+    { "q": 0.25, "x": 0.166666666666667 },
+    { "q": 0.50, "x": 0.5 },
+    { "q": 0.75, "x": 1.5 },
+    { "q": 0.90, "x": 4.5 }
+  ]
+},
+{
+  "expr": "LogLogistic(1.0, 0.5)",
+  "dtype": "LogLogistic",
+  "minimum": 0,
+  "maximum": "inf",
+  "properties": {
+  },
+  "points": [
+    { "x": 0.0123456790123457, "pdf": 3.645, "logpdf": 1.29335636546062, "cdf": 0.1 },
+    { "x": 0.0625, "pdf": 1.28, "logpdf": 0.246860077931526, "cdf": 0.2 },
+    { "x": 0.183673469387755, "pdf": 0.571666666666667, "logpdf": -0.559199208050207, "cdf": 0.3 },
+    { "x": 0.444444444444445, "pdf": 0.27, "logpdf": -1.30933331998376, "cdf": 0.4 },
+    { "x": 1, "pdf": 0.125, "logpdf": -2.07944154167984, "cdf": 0.5 },
+    { "x": 2.25, "pdf": 0.0533333333333334, "logpdf": -2.93119375241642, "cdf": 0.6 },
+    { "x": 5.44444444444445, "pdf": 0.0192857142857143, "logpdf": -3.94839064959902, "cdf": 0.7 },
+    { "x": 16, "pdf": 0.005, "logpdf": -5.29831736654804, "cdf": 0.8 },
+    { "x": 81, "pdf": 0.000555555555555555, "logpdf": -7.49554194388426, "cdf": 0.9 }
+  ],
+  "quans": [
+    { "q": 0.10, "x": 0.0123456790123457 },
+    { "q": 0.25, "x": 0.111111111111111 },
+    { "q": 0.50, "x": 1 },
+    { "q": 0.75, "x": 9 },
+    { "q": 0.90, "x": 81 }
+  ]
+},
+{
+  "expr": "LogLogistic(1.0, 1.0)",
+  "dtype": "LogLogistic",
+  "minimum": 0,
+  "maximum": "inf",
+  "properties": {
+  },
+  "points": [
+    { "x": 0.111111111111111, "pdf": 0.81, "logpdf": -0.210721031315653, "cdf": 0.1 },
+    { "x": 0.25, "pdf": 0.64, "logpdf": -0.44628710262842, "cdf": 0.2 },
+    { "x": 0.428571428571429, "pdf": 0.49, "logpdf": -0.713349887877465, "cdf": 0.3 },
+    { "x": 0.666666666666667, "pdf": 0.36, "logpdf": -1.02165124753198, "cdf": 0.4 },
+    { "x": 1, "pdf": 0.25, "logpdf": -1.38629436111989, "cdf": 0.5 },
+    { "x": 1.5, "pdf": 0.16, "logpdf": -1.83258146374831, "cdf": 0.6 },
+    { "x": 2.33333333333333, "pdf": 0.09, "logpdf": -2.40794560865187, "cdf": 0.7 },
+    { "x": 4, "pdf": 0.04, "logpdf": -3.2188758248682, "cdf": 0.8 },
+    { "x": 9, "pdf": 0.01, "logpdf": -4.60517018598809, "cdf": 0.9 }
+  ],
+  "quans": [
+    { "q": 0.10, "x": 0.111111111111111 },
+    { "q": 0.25, "x": 0.333333333333333 },
+    { "q": 0.50, "x": 1 },
+    { "q": 0.75, "x": 3 },
+    { "q": 0.90, "x": 9 }
+  ]
+},
+{
+  "expr": "LogLogistic(1.0, 2.0)",
+  "dtype": "LogLogistic",
+  "minimum": 0,
+  "maximum": "inf",
+  "properties": {
+  },
+  "points": [
+    { "x": 0.333333333333333, "pdf": 0.54, "logpdf": -0.616186139423817, "cdf": 0.1 },
+    { "x": 0.5, "pdf": 0.64, "logpdf": -0.44628710262842, "cdf": 0.2 },
+    { "x": 0.654653670707977, "pdf": 0.641560597293818, "logpdf": -0.443851637511121, "cdf": 0.3 },
+    { "x": 0.816496580927726, "pdf": 0.587877538267963, "logpdf": -0.531236621026118, "cdf": 0.4 },
+    { "x": 1, "pdf": 0.5, "logpdf": -0.693147180559945, "cdf": 0.5 },
+    { "x": 1.22474487139159, "pdf": 0.391918358845309, "logpdf": -0.936701729134283, "cdf": 0.6 },
+    { "x": 1.52752523165195, "pdf": 0.27495454169735, "logpdf": -1.29114949789833, "cdf": 0.7 },
+    { "x": 2, "pdf": 0.16, "logpdf": -1.83258146374831, "cdf": 0.8 },
+    { "x": 3, "pdf": 0.06, "logpdf": -2.81341071676004, "cdf": 0.9 }
+  ],
+  "quans": [
+    { "q": 0.10, "x": 0.333333333333333 },
+    { "q": 0.25, "x": 0.577350269189626 },
+    { "q": 0.50, "x": 1 },
+    { "q": 0.75, "x": 1.73205080756888 },
+    { "q": 0.90, "x": 3 }
+  ]
+},
+{
+  "expr": "LogLogistic(2.0, 1.0)",
+  "dtype": "LogLogistic",
+  "minimum": 0,
+  "maximum": "inf",
+  "properties": {
+  },
+  "points": [
+    { "x": 0.222222222222222, "pdf": 0.405, "logpdf": -0.903868211875598, "cdf": 0.1 },
+    { "x": 0.5, "pdf": 0.32, "logpdf": -1.13943428318836, "cdf": 0.2 },
+    { "x": 0.857142857142857, "pdf": 0.245, "logpdf": -1.40649706843741, "cdf": 0.3 },
+    { "x": 1.33333333333333, "pdf": 0.18, "logpdf": -1.71479842809193, "cdf": 0.4 },
+    { "x": 2, "pdf": 0.125, "logpdf": -2.07944154167984, "cdf": 0.5 },
+    { "x": 3, "pdf": 0.08, "logpdf": -2.52572864430826, "cdf": 0.6 },
+    { "x": 4.66666666666667, "pdf": 0.045, "logpdf": -3.10109278921182, "cdf": 0.7 },
+    { "x": 8, "pdf": 0.02, "logpdf": -3.91202300542815, "cdf": 0.8 },
+    { "x": 18, "pdf": 0.005, "logpdf": -5.29831736654804, "cdf": 0.9 }
+  ],
+  "quans": [
+    { "q": 0.10, "x": 0.222222222222222 },
+    { "q": 0.25, "x": 0.666666666666667 },
+    { "q": 0.50, "x": 2 },
+    { "q": 0.75, "x": 6 },
+    { "q": 0.90, "x": 18 }
+  ]
+},
+{
+  "expr": "LogLogistic(2.0, 2.0)",
+  "dtype": "LogLogistic",
+  "minimum": 0,
+  "maximum": "inf",
+  "properties": {
+  },
+  "points": [
+    { "x": 0.666666666666667, "pdf": 0.27, "logpdf": -1.30933331998376, "cdf": 0.1 },
+    { "x": 1, "pdf": 0.32, "logpdf": -1.13943428318836, "cdf": 0.2 },
+    { "x": 1.30930734141595, "pdf": 0.320780298646909, "logpdf": -1.13699881807107, "cdf": 0.3 },
+    { "x": 1.63299316185545, "pdf": 0.293938769133981, "logpdf": -1.22438380158606, "cdf": 0.4 },
+    { "x": 2, "pdf": 0.25, "logpdf": -1.38629436111989, "cdf": 0.5 },
+    { "x": 2.44948974278318, "pdf": 0.195959179422654, "logpdf": -1.62984890969423, "cdf": 0.6 },
+    { "x": 3.05505046330389, "pdf": 0.137477270848675, "logpdf": -1.98429667845827, "cdf": 0.7 },
+    { "x": 4, "pdf": 0.08, "logpdf": -2.52572864430826, "cdf": 0.8 },
+    { "x": 6, "pdf": 0.03, "logpdf": -3.50655789731998, "cdf": 0.9 }
+  ],
+  "quans": [
+    { "q": 0.10, "x": 0.666666666666667 },
+    { "q": 0.25, "x": 1.15470053837925 },
+    { "q": 0.50, "x": 2 },
+    { "q": 0.75, "x": 3.46410161513775 },
+    { "q": 0.90, "x": 6 }
+  ]
+},
 {
   "expr": "LogNormal()",
   "dtype": "LogNormal",
diff --git a/test/ref/rdistributions.R b/test/ref/rdistributions.R
index 53623544ba..2bb8c55c84 100644
--- a/test/ref/rdistributions.R
+++ b/test/ref/rdistributions.R
@@ -62,6 +62,7 @@ source("continuous/laplace.R")
 source("continuous/levy.R")
 source("continuous/lindley.R")
 source("continuous/logistic.R")
+source("continuous/loglogistic.R")
 source("continuous/lognormal.R")
 source("continuous/noncentralbeta.R")
 source("continuous/noncentralchisq.R")

From c7e2e4b731a302315930593fde4b080ff59909e1 Mon Sep 17 00:00:00 2001
From: David Widmann <devmotion@users.noreply.github.com>
Date: Mon, 27 Oct 2025 17:28:00 +0100
Subject: [PATCH 12/13] Fix docstring

---
 docs/src/univariate.md                   |  2 +-
 src/univariate/continuous/loglogistic.jl | 10 ++++++----
 2 files changed, 7 insertions(+), 5 deletions(-)

diff --git a/docs/src/univariate.md b/docs/src/univariate.md
index ed6b1c9484..48a90c7a42 100644
--- a/docs/src/univariate.md
+++ b/docs/src/univariate.md
@@ -330,7 +330,7 @@ plotdensity((-4, 8), Logistic, (2, 1)) # hide
 LogLogistic
 ```
 ```@example plotdensity
-plotdensity((0, 2), LogLogistic, (1, 1)) # hide
+plotdensity((0, 2), LogLogistic, (2, 1)) # hide
 ```
 
 ```@docs
diff --git a/src/univariate/continuous/loglogistic.jl b/src/univariate/continuous/loglogistic.jl
index 8a5ba67b16..37b181c0f5 100644
--- a/src/univariate/continuous/loglogistic.jl
+++ b/src/univariate/continuous/loglogistic.jl
@@ -1,11 +1,13 @@
 """
     LogLogistic(α, β)
 
-The *log-logistic distribution* with scale `α` and shape `β` is the distribution of a random variable whose logarithm has a [`Logistic`](@ref) distribution. 
-If ``X \\sim \\operatorname{LogLogistic}(\\alpha, \\beta)`` then ``log(X) \\sim \\operatorname{Logistic}(log(\\alpha), 1/\\beta)``. The probability density function is 
+The *log-logistic distribution* with scale ``\\alpha`` and shape ``\\beta`` is the distribution of a random variable whose logarithm has a [`Logistic`](@ref) distribution. 
+
+If ``X \\sim \\operatorname{LogLogistic}(\\alpha, \\beta)`` then ``\\log(X) \\sim \\operatorname{Logistic}(\\log(\\alpha), 1/\\beta)``.
+The probability density function is 
 
 ```math
-f(x; \\alpha, \\beta) = \\frac{(\\alpha / \\beta)x/\\beta()^(\\alpha - 1)}{(1 + (x/\\beta)^\\alpha)^2}, \\beta > 0, \\alpha > 0
+f(x; \\alpha, \\beta) = \\frac{(\\beta / \\alpha){(x/\\alpha)}^{\\beta - 1}}{{(1 + {(x/\\alpha)}^\\beta)}^2}, \\qquad \\alpha > 0, \\beta > 0.
 ```
 
 ```julia
@@ -18,7 +20,7 @@ shape(d)                 # Get the shape parameter, i.e. β
 
 External links
 
-* [Log logistic distribution on Wikipedia](https://en.wikipedia.org/wiki/Log-logistic_distribution)
+* [Log-logistic distribution on Wikipedia](https://en.wikipedia.org/wiki/Log-logistic_distribution)
 """
 struct LogLogistic{T<:Real} <: ContinuousUnivariateDistribution
     α::T

From 4d24b07553d9c07c679dfffedb34572f403ce3f7 Mon Sep 17 00:00:00 2001
From: David Widmann <devmotion@users.noreply.github.com>
Date: Mon, 27 Oct 2025 17:30:39 +0100
Subject: [PATCH 13/13] Update version to 0.25.123

---
 Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Project.toml b/Project.toml
index ed35734f8f..b460dc8bf8 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "Distributions"
 uuid = "31c24e10-a181-5473-b8eb-7969acd0382f"
 authors = ["JuliaStats"]
-version = "0.25.122"
+version = "0.25.123"
 
 [deps]
 AliasTables = "66dad0bd-aa9a-41b7-9441-69ab47430ed8"