[New copulas] Fréchet-Hoeffding mixture family

src/MiscellaneousCopulas/FHCopula.jl

@@ -0,0 +1,49 @@
+struct MixtureCopula{d,CT1,CT2,T}<:Copula{d} where {CT1 <: Copula{d}, CT2 <: Copula{d}, T}
+    C1::CT1
+    C2::CT2
+    p::T
+    function MixtureCopula(C₁, C₂, w₁, w₂)
+        @assert w₁ >= 0 && w₂ >= 0
+        p = w₁ / (w₁ + w₂)
+        if p >= 0.5
+            new{eltype(C₁),eltype(C₂), eltype(p)}(C₁,C₂,p)
+        else
+            new{eltype(C₂),eltype(C₁), eltype(p)}(C₂,C₁,1-p)
+        end
+    end
+end
+
+function MixtureCopula(CopList,weights)
+    n = length(CopList)
+    if n ==1
+        return CopList[1]
+    elseif n == 2
+        return MixtureCopula(CopList[1],CopList[2], weights[1],weights[2])
+    else
+        return MixtureCopula(
+            CopList[1],
+            MixtureCopula(CopList[2:end],weights[2:end]),
+            weights[1],
+            sum(weights[2:end])
+        )
+    end
+end
+
+
+function Distributions.cdf(C::MixtureCopula,u)
+    return p * Distributions.cdf(C.C1,u) + (1-p) * Distributions.cdf(C.C2,u)
+end
+
+
+
+function Distributions._rand!(rng::Distributions.AbstractRNG, C::MixtureCopula, x::AbstractVector{T}) where T<:Real
+    if rand() < p
+        Distributions._rand!(rng,C.C1,x)
+    else
+        Distribution._rand!(rng,C.C2,x)
+    end
+end
+function Base.rand(rng::Distributions.AbstractRNG,C::MixtureCopula)
+    x = zeros(d)
+    Distributions._rand!(C,x)
+end

test/biv_clayton.jl

@@ -48,8 +48,8 @@ end
     v1 = [0.0, 0.1796053020267749, 0.37796447300922725, 0.6255432421712244, 1.0]
     v2 = [1.0, 0.0, 0.17157287525381, 0.5358983848622453, 1.0]
     for i in 1:5
-        @test cdf(ClaytonCopula(2,2),[x[i],y[i]])==v1[i]
-        @test cdf(ClaytonCopula(2,-0.5),[x[i],y[i]])==v2[i]
+        @test cdf(ClaytonCopula(2,2),[x[i],y[i]]) ≈ v1[i]
+        @test cdf(ClaytonCopula(2,-0.5),[x[i],y[i]]) ≈ v2[i]
     end
 end