Add bindings and tests for WIlliamsonCopulas where needed by the arch…

…idedans.

Project.toml

@@ -27,7 +27,7 @@ Roots = "1, 2"
 SpecialFunctions = "2"
 StatsBase = "0.33, 0.34"
 TaylorSeries = "0.12, 0.13, 0.14, 0.15"
-WilliamsonTransforms = "0.0"
+WilliamsonTransforms = "0.0.3 - 0"
 julia = "1.6"
 
 [extras]

src/ArchimedeanCopulas/AMHCopula.jl

@@ -21,10 +21,12 @@ It has a few special cases:
 struct AMHCopula{d,T} <: ArchimedeanCopula{d}
     θ::T
     function AMHCopula(d,θ)
-        if (θ < -1) || (θ > 1)
+        if (θ < -1) || (θ >= 1)
             throw(ArgumentError("Theta must be in [-1,1)"))
         elseif θ == 0
             return IndependentCopula(d)
+        elseif θ < 0
+            return WilliamsonCopula(t -> (1-θ)/(exp(t)-θ),d)
         else
             return new{d,typeof(θ)}(θ)
         end

src/ArchimedeanCopulas/ClaytonCopula.jl

@@ -27,6 +27,9 @@ struct ClaytonCopula{d,T} <: ArchimedeanCopula{d}
             throw(ArgumentError("Theta must be greater than -1/(d-1)"))
         elseif θ == -1/(d-1)
             return WCopula(d)
+        elseif θ < 0
+            return WilliamsonCopula(
+                t -> max(1+θ*t,zero(t))^(-1/θ),d)
         elseif θ == 0
             return IndependentCopula(d)
         elseif θ == Inf
@@ -36,8 +39,8 @@ struct ClaytonCopula{d,T} <: ArchimedeanCopula{d}
         end
     end
 end
-ϕ(  C::ClaytonCopula,      t) = (1+sign(C.θ)*t)^(-1/C.θ)
-ϕ⁻¹(C::ClaytonCopula,      t) = sign(C.θ)*(t^(-C.θ)-1)
+ϕ(  C::ClaytonCopula,      t) = max(1+C.θ*t,0)^(-1/C.θ)
+ϕ⁻¹(C::ClaytonCopula,      t) = (t^(-C.θ)-1)/C.θ
 radial_dist(C::ClaytonCopula) = Distributions.Gamma(1/C.θ,1) # Currently fails for negative thetas ! thus negtatively correlated clayton copulas cannot be sampled...
 τ(C::ClaytonCopula) = ifelse(isfinite(C.θ), C.θ/(C.θ+2), 1)
 τ⁻¹(::Type{ClaytonCopula},τ) = ifelse(τ == 1,Inf,2τ/(1-τ))

test/archimedean_tests.jl

@@ -1,5 +1,5 @@
 
-@testitem "test bijection" begin
+@testitem "Test of τ ∘ τ_inv bijection" begin
     using Random 
     Random.seed!(123)
     taus = [0.0, 0.1, 0.5, 0.9, 1.0]
@@ -17,3 +17,49 @@
         end
     end
 end
+
+
+@testitem "AMHCopula - Test sampling all cases" begin
+    for d in 2:10
+        for θ ∈ [-1.0,-rand(),0.0,rand()]
+            rand(AMHCopula(d,θ),10)
+        end
+    end
+    @test true
+end
+@testitem "ClaytonCopula - Test sampling all cases" begin
+    rand(ClaytonCopula(2,-1),10)
+    for d in 2:10
+        for θ ∈ [-1/(d-1) * rand(),0.0,-log(rand()), Inf]
+            rand(ClaytonCopula(d,θ),10)
+        end
+    end
+    @test true
+end
+@testitem "FrankCopula - Test sampling all cases" begin
+    rand(FrankCopula(2,-Inf),10)
+    for d in 2:10
+        for θ ∈ [log(rand()),0.0,rand(),1.0,-log(rand()), Inf]
+            rand(FrankCopula(d,θ),10)
+        end
+    end
+    @test true
+end
+@testitem "GumbelCopula - Test sampling all cases" begin
+    for d in 2:10
+        for θ ∈ [1.0,1-log(rand()), Inf]
+            @show d, θ
+            rand(GumbelCopula(d,θ),10)
+        end
+    end
+    @test true
+end
+@testitem "JoeCopula - Test sampling all cases" begin
+    for d in 2:10
+        for θ ∈ [1.0,1-log(rand()), Inf]
+            rand(JoeCopula(d,θ),10)
+        end
+    end
+    @test true
+end
+