Fix generics for cdf, \tau and \rho (#133)

docs/src/dependence_measures.md

@@ -3,6 +3,11 @@
 
 Although the copula is an object that summarizes completely the dependence structure of any random vector, it is an infinite dimensional object and the interpretation of its properties can be difficult when the dimension gets high. Therefore, the literature has come up with some quantification of the dependence structure that might be used as univariate summaries, of course imperfect, of certain properties of the copula at hand. 
 
+
+!!! note "Unfinished work"
+    Unfortunately these dependence measures are not yet well-specified in the package and their implementation is experimental for the moment. These functions might change in the future, in particular see https://github.com/lrnv/Copulas.jl/issues/134 for future improvements. 
+
+
 ## Kendall's Tau 
 
 > **Definition (Kendall' τ):** For a copula $C$ with a density $c$, Kendall's τ is defined as: 
@@ -52,9 +57,6 @@ The graph of $u \to \chi(u)$ over $[\frac{1}{2},1]$ is an interesting tool to as
 
 All these coefficients quantify the behavior of the dependence structure, generally or in the extremes, and are therefore widely used in the literature either as verification tools to assess the quality of fits, or even as parameters. Many parametric copulas families have simple surjections, injections, or even bijections between these coefficients and their parametrization, allowing matching procedures of estimation (a lot like moments matching algorithm for fitting standard random variables).
 
-!!! note "Unfinished work"
-    Unfortunately these coefficients are not yet well-specified in the package and implemented for all dependence structure, there is still work to do. 
-
 
 ```@bibliography
 Pages = ["dependence_measures.md"]

src/ArchimedeanCopula.jl

@@ -131,11 +131,6 @@ end
 function τ⁻¹(::Type{T},τ_val) where {T<:ArchimedeanCopula}
     return τ⁻¹(generatorof(T),τ_val)
 end
-ρ(C::ArchimedeanCopula{d,TG}) where {d,TG} = ρ(C.G)
-function ρ⁻¹(::Type{T},ρ_val) where {T<:ArchimedeanCopula}
-    return ρ⁻¹(generatorof(T),ρ_val)
-end
-
 
 ################################################################################################
 ################                                                                ################

src/Copula.jl

@@ -18,15 +18,20 @@ function Distributions.cdf(C::Copula{d},A::AbstractMatrix) where d
     return [_cdf(C,u) for u in eachcol(A)]
 end
 function _cdf(C::CT,u) where {CT<:Copula}
+    if any(iszero.(u))
+        return zero(u[1])
+    elseif all(isone.(u))
+        return one(u[1])
+    end
     f(x) = Distributions.pdf(C,x)
     z = zeros(eltype(u),length(C))
-    return Cubature.pcubature(f,z,u,reltol=sqrt(eps()))[1]
+    return Cubature.hcubature(f,z,u,reltol=sqrt(eps()))[1]
 end
 function ρ(C::Copula{d}) where d
     F(x) = Distributions.cdf(C,x)
     z = zeros(d)
     i = ones(d)
-    r = Cubature.pcubature(F,z,i,reltop=sqrt(eps()))[1]
+    r = Cubature.hcubature(F,z,i,reltol=sqrt(eps()))[1]
     return 12*r-3
 end
 function τ(C::Copula)

test/archimedean_tests.jl

@@ -126,9 +126,9 @@ end
 
 @testitem "Archimedeans - Spearman correlation" begin
 
-    @test_broken Copulas.ρ(ClaytonCopula(2,3.)) ≈ 0.78645 atol=1.0e-4
-    @test_broken Copulas.ρ(ClaytonCopula(2,0.001)) ≈ 0. atol=1.0e-2
-    @test_broken Copulas.ρ(GumbelCopula(2,3.)) ≈ 0.8489 atol=1.0e-4
+    @test Copulas.ρ(ClaytonCopula(2,3.)) ≈ 0.78645 atol=1.0e-4
+    @test Copulas.ρ(ClaytonCopula(2,0.001)) ≈ 0. atol=1.0e-2
+    @test Copulas.ρ(GumbelCopula(2,3.)) ≈ 0.8489 atol=1.0e-4
 
     @test_broken Copulas.ρ⁻¹(ClaytonCopula, 1/3) ≈ 0.58754 atol=1.0e-5
     @test_broken Copulas.ρ⁻¹(ClaytonCopula, 0.01) ≈ 0. atol=1.0e-1

test/kendall_tau_notnan.jl

@@ -0,0 +1,39 @@
+@testitem "Check non-nan in kendall taus and spearman rhos." begin
+    using Copulas, Distributions
+
+    cops = (
+        IndependentCopula(3),
+        AMHCopula(3,0.6),
+        AMHCopula(4,-0.3),
+        ClaytonCopula(2,-0.7),
+        ClaytonCopula(3,-0.1),
+        ClaytonCopula(4,7.),
+        FrankCopula(2,-5.),
+        FrankCopula(3,12.),
+        FrankCopula(4,6.),
+        FrankCopula(4,150.),
+        JoeCopula(3,7.),
+        GumbelCopula(4,7.),
+        GumbelCopula(4,20.),
+        GumbelBarnettCopula(3,0.7),
+        InvGaussianCopula(4,0.05),
+        InvGaussianCopula(3,8.),
+        GaussianCopula([1 0.5; 0.5 1]),
+        # TCopula(4, [1 0.5; 0.5 1]), # this one takes a while. 
+        FGMCopula(2,1),
+        MCopula(4),
+        WCopula(2),
+        PlackettCopula(2.0),
+        EmpiricalCopula(randn(2,100),pseudo_values=false),
+        SurvivalCopula(ClaytonCopula(2,-0.7),(1,2)),
+        RafteryCopula(2, 0.2),
+        RafteryCopula(3, 0.5),
+        # Others ? Yes probably others too ! 
+    )
+
+    for C in cops
+        @show C
+        @test !isnan(Copulas.τ(C))
+    end
+    @test_broken Copulas.τ(ArchimedeanCopula(2,i𝒲(LogNormal(),2))) # not implemented. 
+end

test/margins_uniformity.jl

@@ -121,20 +121,12 @@
                 u = ones(d)
                 for val in [0,1,rand(rng,10)...]
                     u[i] = val
-                    if typeof(C)<:TCopula
-                        @test_broken cdf(C,u) ≈ val
-                    else
-                        @test cdf(C,u) ≈ val atol=1e-5
-                    end
+                    @test cdf(C,u) ≈ val atol=1e-5
                 end
                 # extra check for zeros: 
                 u = rand(rng,d)
                 u[i] = 0
-                if typeof(C)<:TCopula
-                    @test_broken cdf(C,u) ≈ val
-                else
-                    @test iszero(cdf(C,u))
-                end
+                @test iszero(cdf(C,u))
             end
         end
 

test/some_tests.jl

@@ -48,22 +48,16 @@ end
         ClaytonCopula(4,7.0),
         GaussianCopula([1 0.3; 0.3 1]),
         FrankCopula(5,6.0),
-        AMHCopula(3,0.7)
+        AMHCopula(3,0.7),
+        TCopula(4,[1 0.5; 0.5 1])
     )
 
-
     for C in Copula_Zoo
         d = length(C)
 
         @test cdf(C,ones(d)) ≈ 1
         @test cdf(C,zeros(d)) ≈ 0    
     end
-
-    for C in (TCopula(4,[1 0.5; 0.5 1]),)
-        d = length(C)
-        @test_broken cdf(C,ones(d)) ≈ 1
-        @test_broken cdf(C,zeros(d)) ≈ 0    
-    end
 end
 
 @testitem "pdf/cdf archimedean" begin
@@ -126,7 +120,7 @@ end
     using StableRNGs
     rng = StableRNG(123)
 
-    for C in (ClaytonCopula(4,7.0),GumbelCopula(2, 1.2))
+    for C in (ClaytonCopula(4,7.0),GumbelCopula(2, 1.2), TCopula(4,[1 0.5; 0.5 1]))
         d = length(C)
         u = zeros(d)
         v = ones(d)
@@ -139,20 +133,6 @@ end
         end
         @test Copulas.measure(C,u,v) >= 0
     end
-
-    for C in (TCopula(4,[1 0.5; 0.5 1]),)
-        d = length(C)
-        u = zeros(d)
-        v = ones(d)
-
-        @test_broken Copulas.measure(C,u,v) >= 0
-
-        for i in 1:d
-            u[i] = rand(rng)
-            v[i] = u[i] + rand(rng)*(1-u[i])
-        end
-        @test_broken Copulas.measure(C,u,v) >= 0
-    end
 end