Gamma measure

src/MeasureTheory.jl

@@ -83,6 +83,7 @@ include("parameterized/laplace.jl")
 include("parameterized/uniform.jl")
 include("parameterized/beta.jl")
 include("parameterized/dirichlet.jl")
+include("parameterized/gamma.jl")
 include("parameterized/gumbel.jl")
 include("parameterized/exponential.jl")
 include("parameterized/mvnormal.jl")

src/parameterized/gamma.jl

@@ -0,0 +1,41 @@
+# Gamma distribution
+
+# REFERENCES
+# https://mc-stan.org/docs/2_27/functions-reference/gamma-distribution.html
+# https://en.wikipedia.org/wiki/Gamma_distribution
+# https://juliastats.org/Distributions.jl/stable/univariate/#Distributions.Gamma
+
+export Gamma
+
+@parameterized Gamma(α, θ) ≪ Lebesgue(ℝ₊)
+
+@kwstruct Gamma(α, θ)
+@kwstruct Gamma(α, β)
+
+@kwalias Gamma [
+    a     => α
+    alpha => α
+    shape => α
+    b     => β
+    beta  => β
+    rate  => β
+    theta => θ
+    scale => θ
+]
+
+TV.as(::Gamma) = asℝ₊
+
+function logdensity(d::Gamma{(:α, :θ)}, x)
+    return (d.α - 1) * log(x) - x / d.θ - d.α * log(d.θ) - loggamma(d.α)
+end
+
+function logdensity(d::Gamma{(:α, :β)}, x)
+    return (d.α - 1) * log(x) - x * d.β + d.α * log(d.β) - loggamma(d.α)
+end
+
+distproxy(d::Gamma{(:α, :θ)}) = Dists.Gamma(d.α, d.θ)
+distproxy(d::Gamma{(:α, :β)}) = Dists.Gamma(d.α, 1/d.β)
+
+asparams(::Type{<:Gamma}, ::Val{:α}) = asℝ₊
+asparams(::Type{<:Gamma}, ::Val{:β}) = asℝ₊
+asparams(::Type{<:Gamma}, ::Val{:θ}) = asℝ₊