[New Generator] PowerGenerator from any other generator

docs/src/archimedean/available_models.md

@@ -8,6 +8,12 @@ CurrentModule = Copulas
 ```@docs; canonical=false
 WilliamsonGenerator
 ```
+
+## `PowerGenerator`
+```@docs
+PowerGenerator
+```
+
 ## `IndependentGenerator`
 ```@docs
 IndependentGenerator

src/Copulas.jl

@@ -64,6 +64,7 @@ module Copulas
     include("Generator/UnivariateGenerator/GumbelGenerator.jl")
     include("Generator/UnivariateGenerator/InvGaussianGenerator.jl")
     include("Generator/UnivariateGenerator/JoeGenerator.jl")
+    include("Generator/DistordedGenerator/PowerGenerator.jl")
 
     # Archimedean copulas
     include("ArchimedeanCopula.jl")

src/Generator.jl

@@ -51,4 +51,5 @@ williamson_dist(G::Generator, d) = WilliamsonTransforms.𝒲₋₁(t -> ϕ(G,t),
 
 
 abstract type UnivariateGenerator <: Generator end
-abstract type ZeroVariateGenerator <: Generator end
+abstract type ZeroVariateGenerator <: Generator end
+abstract type DistordedGenerator <: Generator end

src/Generator/DistordedGenerator/PowerGenerator.jl

@@ -0,0 +1,45 @@
+"""
+    PowerGenerator{T, TG}
+
+Fields:
+* `G::Generator` - another generator
+* `α::Real` - parameter, the inner power, positive
+* `β::Real` - parameter, the outer power, positive
+
+Constructor
+
+    PowerGenerator(G, α, β)
+
+    The inner/outer power generator based on the generator ϕ given by 
+
+```math
+\\phi_{\\alpha,\\beta}(t) = \\phi(t^\\alpha)^\\beta
+```
+
+It keeps the monotony of ϕ. 
+
+It has a few special cases: 
+    - When α = 1 and β = 1, it returns G.
+
+References : 
+* [nelsen2006](@cite) Nelsen, R. B. (2006). An introduction to copulas. Springer, theorem 4.5.1 p141
+"""
+struct PowerGenerator{TG,T} <: DistordedGenerator
+    G::TG
+    α::T
+    β::T
+    function PowerGenerator(G, α, β)
+        @assert α > 0
+        @assert β > 0
+        if α == 1 && β == 1
+            return G
+        end
+        α,β = promote(α,β)
+        return new{typeof(G),typeof(β)}(G, α, β)
+    end
+end
+max_monotony(G::PowerGenerator) = max_monotony(G.G)
+ϕ(  G::PowerGenerator, t) = ϕ(G.G,t^G.α)^G.β
+ϕ⁻¹(G::PowerGenerator, t) = ϕ⁻¹(G.G, t^(1/G.β))^(1/G.α)
+
+

test/archimedean_tests.jl

@@ -286,6 +286,27 @@ end
     @test true
 end
 
+@testitem "PowerGenerator - sampling,pdf,cdf,fit" begin
+    using StableRNGs
+    using Distributions
+    rng = StableRNG(123)
+    for d in 2:10
+        for G ∈ (
+            Copulas.GumbelGenerator(1.7),
+            Copulas.ClaytonGenerator(1.8),
+            # others ?
+        )
+            C = ArchimedeanCopula(d,Copulas.PowerGenerator(G,1,2))
+            # C = InvGaussianCopula(d,θ)
+            data = rand(rng,C,100)
+            # @test all(pdf(C,data) .>= 0)
+            # @test all(0 .<= cdf(C,data) .<= 1)
+            # fit(GumbelCopula,data)
+        end
+    end
+    @test true
+end
+
 @testitem "Testing empirical tail values of certain copula samples" begin
     using StableRNGs
     using Distributions