Add automatic tests (#93)

Also fixes a few bugs

src/ArchimedeanCopula.jl

@@ -93,27 +93,26 @@ end
 #     return 4*Distributions.expectation(r -> ϕ(C,r), williamson_dist(C)) - 1
 # end
 
-function _archi_rand!(rng,C::ArchimedeanCopula{d},R,x) where d
-    # x is assumed to already be random exponentials produced by Random.randexp
-    r = rand(rng,R)
-    sx = sum(x)
-    for i in 1:d
-        x[i] = ϕ(C,r * x[i]/sx)
-    end
-end
-
 function Distributions._rand!(rng::Distributions.AbstractRNG, C::CT, x::AbstractVector{T}) where {T<:Real, CT<:ArchimedeanCopula}
     # By default, we use the williamson sampling. 
     Random.randexp!(rng,x)
-    _archi_rand!(rng,C,williamson_dist(C),x)
+    r = rand(rng,williamson_dist(C))
+    sx = sum(x)
+    for i in 1:length(C)
+        x[i] = ϕ(C,r * x[i]/sx)
+    end
     return x
 end
 function Distributions._rand!(rng::Distributions.AbstractRNG, C::CT, A::DenseMatrix{T}) where {T<:Real, CT<:ArchimedeanCopula}
     # More efficient version that precomputes the williamson transform on each call to sample in batches: 
     Random.randexp!(rng,A)
-    R = williamson_dist(C)
-    for i in 1:size(A,2)
-        _archi_rand!(rng,C,R,view(A,:,i))
+    n = size(A,2)
+    r = rand(rng,williamson_dist(C),n)
+    for i in 1:n
+        sx = sum(A[:,i])
+        for j in 1:length(C)
+            A[j,i] = ϕ(C,r[i] * A[j,i]/sx)
+        end
     end
     return A
 end
@@ -123,8 +122,9 @@ function Distributions.fit(::Type{CT},u) where {CT <: ArchimedeanCopula}
     τ = StatsBase.corkendall(u')
     # Then the off-diagonal elements of the matrix should be averaged: 
     avgτ = (sum(τ) .- d) / (d^2-d)
-    θ = τ⁻¹(CT,avgτ)
-    return CT(d,θ)
+    GT = generatorof(CT)
+    θ = τ⁻¹(GT,avgτ)
+    return ArchimedeanCopula(d,GT(θ))
 end
 
 τ(C::ArchimedeanCopula{d,TG}) where {d,TG} = τ(C.G)

src/Generator.jl

@@ -44,10 +44,10 @@ function ϕ⁽ᵏ⁾(G::Generator, k, t)
 end
 williamson_dist(G::Generator, d) = WilliamsonTransforms.𝒲₋₁(t -> ϕ(G,t),d)
 
-τ(G::Generator) = @error("This generator has no kendall tau implemented.")
-ρ(G::Generator) = @error ("This generator has no Spearman rho implemented.")
-τ⁻¹(G::Generator, τ_val) = @error("This generator has no inverse kendall tau implemented.")
-ρ⁻¹(G::Generator, ρ_val) = @error ("This generator has no inverse Spearman rho implemented.")
+# τ(G::Generator) = @error("This generator has no kendall tau implemented.")
+# ρ(G::Generator) = @error ("This generator has no Spearman rho implemented.")
+# τ⁻¹(G::Generator, τ_val) = @error("This generator has no inverse kendall tau implemented.")
+# ρ⁻¹(G::Generator, ρ_val) = @error ("This generator has no inverse Spearman rho implemented.")
 
 
 abstract type UnivariateGenerator <: Generator end

src/Generator/WilliamsonGenerator.jl

@@ -1,5 +1,6 @@
 """
     WilliamsonGenerator{TX}
+    i𝒲{TX}
 
 Fields:
 * `X::TX` -- a random variable that represents its williamson d-transform
@@ -8,8 +9,9 @@ Fields:
 Constructor
 
     WilliamsonGenerator(X::Distributions.UnivariateDistribution, d)
+    i𝒲(X::Distributions.UnivariateDistribution,d)
 
-The `WilliamsonGenerator` allows to construct a d-monotonous archimedean generator from a positive random variable `X::Distributions.UnivariateDistribution`. The transformation, wich is called the inverse williamson transformation, is implemented in [WilliamsonTransforms.jl](https://www.github.com/lrnv/WilliamsonTransforms.jl). 
+The `WilliamsonGenerator` (alias `i𝒲`) allows to construct a d-monotonous archimedean generator from a positive random variable `X::Distributions.UnivariateDistribution`. The transformation, wich is called the inverse williamson transformation, is implemented in [WilliamsonTransforms.jl](https://www.github.com/lrnv/WilliamsonTransforms.jl). 
 
 For a univariate non-negative random variable ``X``, with cumulative distribution function ``F`` and an integer ``d\\ge 2``, the Williamson-d-transform of ``X`` is the real function supported on ``[0,\\infty[`` given by:
 
@@ -45,5 +47,11 @@ struct WilliamsonGenerator{TX} <: Generator
 end
 const i𝒲 = WilliamsonGenerator
 max_monotony(G::WilliamsonGenerator) = G.d
-williamson_dist(G::WilliamsonGenerator) = G.X
+function williamson_dist(G::WilliamsonGenerator, d)
+    if d == G.d 
+        return G.X
+    end
+    # what about d < G.d ? Mayeb we can do some frailty stuff ? 
+    return WilliamsonTransforms.𝒲₋₁(t -> ϕ(G,t),d)
+end
 ϕ(G::WilliamsonGenerator, t) = WilliamsonTransforms.𝒲(G.X,G.d)(t)

src/MiscellaneousCopulas/EmpiricalCopula.jl

@@ -20,17 +20,17 @@ struct EmpiricalCopula{d,MT} <: Copula{d}
     u::MT
 end
 Base.eltype(C::EmpiricalCopula{d,MT}) where {d,MT} = Base.eltype(C.u)
-function EmpiricalCopula(u;pseudos=true)
+function EmpiricalCopula(u;pseudo_values=true)
     d = size(u,1)
-    if !pseudos
+    if !pseudo_values
         u = pseudos(u)
     else
         @assert all(0 .<= u .<= 1)
     end
     return EmpiricalCopula{d,typeof(u)}(u)
 end
 function _cdf(C::EmpiricalCopula{d,MT},u) where {d,MT}
-   return mean(all(C.u .<= u,dims=1)) # might not be very efficient implementation. 
+   return StatsBase.mean(all(C.u .<= u,dims=1)) # might not be very efficient implementation. 
 end
 function Distributions._rand!(rng::Distributions.AbstractRNG, C::EmpiricalCopula{d,MT}, x::AbstractVector{T}) where {d,MT,T<:Real}
     x .= C.u[:,Distributions.rand(rng,axes(C.u,2),1)[1]]

src/MiscellaneousCopulas/RafteryCopula.jl

@@ -40,7 +40,15 @@ struct RafteryCopula{d, P} <: Copula{d}
 end
 Base.eltype(R::RafteryCopula) = eltype(R.θ)
 
-function _cdf(R::RafteryCopula{d,P}, u::Vector{T}) where {d,P,T}
+function _cdf(R::RafteryCopula{d,P}, u) where {d,P}
+
+    if any(iszero,u)
+        return zero(u[1])
+    end
+    if all(isone,u)
+        return one(u[1])
+    end
+
     # Order the vector u
     u_ordered = sort(u)
 

src/MiscellaneousCopulas/SurvivalCopula.jl

@@ -45,7 +45,16 @@ function reverse(u,idx)
     reverse!(v,idx)
     return v
 end
-_cdf(C::SurvivalCopula{d,CT,VI},u) where {d,CT,VI} = _cdf(C.C,reverse(u,C.indices))
+function _cdf(C::SurvivalCopula{d,CT,VI},u) where {d,CT,VI}
+    i = C.indices[end]
+    newC = SurvivalCopula(C.C,C.indices[1:end-1])
+    v = deepcopy(u)
+    v[i] = 1 - v[i]
+    r2 = _cdf(newC,v)
+    v[i] = 1
+    r1 = _cdf(newC,v)
+    return r1 - r2
+end 
 Distributions._logpdf(C::SurvivalCopula{d,CT,VI},u) where {d,CT,VI} = Distributions._logpdf(C.C,reverse(u,C.indices))
 function Distributions._rand!(rng::Distributions.AbstractRNG, C::SurvivalCopula{d,CT,VI}, x::AbstractVector{T}) where {d,CT,VI,T}
     Distributions._rand!(rng,C.C,x)

test/archimedean_tests.jl

@@ -161,7 +161,7 @@ end
     using StableRNGs
     using Distributions
     rng = StableRNG(123)
-    for d in 2:10
+    for d in 2:5
         for θ ∈ [-1.0,-rand(rng),0.0,rand(rng)]
             C = AMHCopula(d,θ)
             data = rand(rng,C,100)
@@ -181,7 +181,7 @@ end
     @test all(pdf(C0,data0) .>= 0)
     @test all(0 .<= cdf(C0,data0) .<= 1)
     fit(ClaytonCopula,data0)
-    for d in 2:10
+    for d in 2:5
         for θ ∈ [-1/(d-1) * rand(rng),0.0,-log(rand(rng)), Inf]
             C = ClaytonCopula(d,θ)
             data = rand(rng,C,100)
@@ -212,7 +212,7 @@ end
     fit(FrankCopula,data1)
 
 
-    for d in 2:10
+    for d in 2:5
         for θ ∈ [1.0,1-log(rand(rng)), Inf]
             C = FrankCopula(d,θ)
             data = rand(rng,C,10000)
@@ -227,7 +227,7 @@ end
     using StableRNGs
     using Distributions
     rng = StableRNG(123)
-    for d in 2:10
+    for d in 2:5
         for θ ∈ [1.0,1-log(rand(rng)), Inf]
             C = GumbelCopula(d,θ)
             data = rand(rng,C,100)
@@ -242,7 +242,7 @@ end
     using StableRNGs
     using Distributions
     rng = StableRNG(123)
-    for d in 2:10
+    for d in 2:5
         for θ ∈ [1.0,1-log(rand(rng)), Inf]
             C = JoeCopula(d,θ)
             data = rand(rng,C,100)
@@ -258,7 +258,7 @@ end
     using StableRNGs
     using Distributions
     rng = StableRNG(123)
-    for d in 2:10
+    for d in 2:5
         for θ ∈ [0.0,rand(rng),1.0]
             C = GumbelBarnettCopula(d,θ)
             data = rand(rng,C,100)
@@ -274,7 +274,7 @@ end
     using StableRNGs
     using Distributions
     rng = StableRNG(123)
-    for d in 2:10
+    for d in 2:5
         for θ ∈ [rand(rng),1.0, -log(rand(rng))]
             C = InvGaussianCopula(d,θ)
             data = rand(rng,C,100)