First sketch

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 : 
+    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)
+
+