fix: ClosedWilliamsProduct for Exponetial on LogNormal

Author: Nimrais

src/Exponential/Exponential.jl

@@ -32,7 +32,7 @@ function mean(::ClosedWilliamsProduct, q::Exponential, p::ExpLogSquare)
     return 1/(2*σ^2)*(-1/λ*(-2*(eulergamma+μ) + log(λ)) - log(λ)/λ)
 end
 
-function mean(::ClosedFormExpectation, q::Exponential, p::LogNormal)
+function mean(::ClosedWilliamsProduct, q::Exponential, p::LogNormal)
     μ, σ = p.μ, p.σ
     λ = mean(q)
     return 1/(2*σ^2)*(-1/λ*(-2*(eulergamma+μ) + log(λ)) - log(λ)/λ) - 1/λ

test/Exponential/williams_tests.jl

@@ -47,7 +47,7 @@ end
     end
 end
 
-@testitem "meanlog(::ClosedWilliamsProduct, q::Exponential, p::LogNormal)" begin
+@testitem "mean(::ClosedWilliamsProduct, q::Exponential, p::LogNormal)" begin
     using Distributions
     using ClosedFormExpectations
     using StableRNGs
@@ -64,12 +64,11 @@ end
         μ = rand(rng)*10
         σ = rand(rng)*10
         λ = rand(rng)*10
-        N = 10^7
+        N = 10^6
         samples = rand(rng, Exponential(λ), 10^6)
         fn(x)  = logpdf(LogNormal(μ, σ), x)
         williams_product = map(x -> score(Exponential(λ), x)*fn(x), samples)
-        expectation = mean(ClosedWilliamsProduct(), Exponential(λ), ExpLogSquare(μ, σ))
-        @show mean(williams_product)
-        @show expectation
+        expectation = mean(ClosedWilliamsProduct(), Exponential(λ), LogNormal(μ, σ))
+        @test sigma_rule(expectation, mean(williams_product), std(williams_product), N)
     end
 end