Implement ExpGamma sampler (draft)

src/samplers.jl

@@ -20,6 +20,7 @@ for fname in ["aliastable.jl",
               "poisson.jl",
               "exponential.jl",
               "gamma.jl",
+              "expgamma.jl",
               "multinomial.jl",
               "vonmises.jl",
               "vonmisesfisher.jl",

src/samplers/expgamma.jl

@@ -0,0 +1,57 @@
+# These are used to bypass subnormals when sampling from
+
+# Inverse Power sampler
+# uses the x*u^(1/a) trick from Marsaglia and Tsang (2000) for when shape < 1
+struct ExpGammaIPSampler{S<:Sampleable{Univariate,Continuous},T<:Real} <: Sampleable{Univariate,Continuous}
+    s::S #sampler for Gamma(1+shape,scale)
+    nia::T #-1/scale
+end
+
+ExpGammaIPSampler(d::Gamma) = ExpGammaIPSampler(d, GammaMTSampler)
+function ExpGammaIPSampler(d::Gamma, ::Type{S}) where {S<:Sampleable}
+    shape_d = shape(d)
+    sampler = S(Gamma{partype(d)}(1 + shape_d, scale(d)))
+    return ExpGammaIPSampler(sampler, -inv(shape_d))
+end
+
+function rand(rng::AbstractRNG, s::ExpGammaIPSampler)
+    x = log(rand(rng, s.s))
+    e = randexp(rng, typeof(x))
+    return muladd(s.nia, e, x)
+end
+
+
+# Small Shape sampler
+# From Liu, C., Martin, R., and Syring, N. (2015) for when shape < 0.3
+struct ExpGammaSSSampler{T<:Real} <: Sampleable{Univariate,Continuous}
+    α::T
+    θ::T
+    λ::T
+    ω::T
+    ωω::T
+end
+
+function ExpGammaSSSampler(d::Gamma)
+    α = shape(d)
+    ω = α / MathConstants.e / (1 - α)
+    return ExpGammaSSSampler(promote(
+        α,
+        scale(d),
+        inv(α) - 1,
+        ω,
+        inv(ω + 1)
+    )...)
+end
+
+function rand(rng::AbstractRNG, s::ExpGammaSSSampler{T})::Float64 where T
+    flT = float(T)
+    while true
+        U = rand(rng, flT)
+        z = (U <= s.ωω) ? -log(U / s.ωω) : log(rand(rng, flT)) / s.λ
+        h = exp(-z - exp(-z / s.α))
+        η = z >= zero(T) ? exp(-z) : s.ω * s.λ * exp(s.λ * z)
+        if h / η > rand(rng, flT)
+            return s.θ - z / s.α
+        end
+    end
+end