new dispatching of correlations

README.md

@@ -185,46 +185,49 @@ of Ali-Mikhail-Haq Copula', Applied Mathematical Sciences, Vol. 4, 2010, no. 14,
 
 
 ```julia
-julia> simulate_copula(5, Clayton_cop(3, 3.))
+julia> Random.seed!(43);
+
+julia> c = Clayton_cop(3, 3.)
+Clayton_cop(3, 3.0)
+
+julia> simulate_copula(5, c)
 5×3 Array{Float64,2}:
- 0.565271    0.930131    0.781448  
- 0.00653614  0.00723128  0.00301186
- 0.0526504   0.0265819   0.0202293
- 0.835776    0.485913    0.35429   
- 0.760815    0.979532    0.635902  
+ 0.740919   0.936613  0.968594
+ 0.369025   0.698884  0.586236
+ 0.0701388  0.185901  0.0890538
+ 0.535579   0.516761  0.538476
+ 0.487668   0.549494  0.804122  
 ```
 
-The optional third `String` parameter is used to compute `θ` from the expected `Kendall` or `Speraman` cross-correlation. Here only positive correlations are supported, and there are some limitations are for the Ali-Mikhail-Haq copula due to limitations on `θ` there.
+The optional third empty type `<: CorrelationType` parameter is used to compute `θ` from the expected Kendall - `KendallCorrelation` or Speraman
+`SpearmanCorrelation` cross-correlation.
+Here only positive correlations are supported, and there are some limitations are for the Ali-Mikhail-Haq copula due to limitations on `θ` there.
 
 
 ```julia
-julia> Random.seed!(43);
-
-julia> c = Clayton_cop(3, 0.5, "Kendall")
+julia> c = Clayton_cop(3, 0.5, KendallCorrelation)
 Clayton_cop(3, 2.0)
 
 julia> x = simulate_copula(500_000, c);
 
 julia> corkendall(x)
 3×3 Array{Float64,2}:
- 1.0       0.49955   0.499212
- 0.49955   1.0       0.499466
- 0.499212  0.499466  1.0   
+ 1.0       0.500576  0.499986
+ 0.500576  1.0       0.501574
+ 0.499986  0.501574  1.0      
 ```
 
 ```julia
-julia> Random.seed!(43);
-
-julia> c = Clayton_cop(3, 0.5, "Spearman")
+julia> c = Clayton_cop(3, 0.5, SpearmanCorrelation)
 Clayton_cop(3, 1.0760904048732394)
 
 julia> x = simulate_copula(500_000, c);
 
 julia> corspearman(x)
 3×3 Array{Float64,2}:
- 1.0       0.499801  0.498785
- 0.499801  1.0       0.498891
- 0.498785  0.498891  1.0  
+ 1.0       0.499662  0.499637
+ 0.499662  1.0       0.500228
+ 0.499637  0.500228  1.0   
 ```
 The reversed Gumbel, Clayton and Ali-Mikhail-Haq copulas are supported as well:
 
@@ -250,16 +253,16 @@ julia> Random.seed!(43);
 
 julia> simulate_copula(10, c)
 10×2 Array{Float64,2}:
- 0.0838518  0.0246107
- 0.753705   0.845248
- 0.0135262  0.149148
- 0.815509   0.906639
- 0.575087   0.63889  
- 0.0574951  0.140628
- 0.314763   0.638385
- 0.135894   0.279956
- 0.623248   0.603208
- 0.0302191  0.0887757
+ 0.246822   0.0735546
+ 0.0214448  0.154414
+ 0.453721   0.598829
+ 0.87328    0.91861  
+ 0.896485   0.899053
+ 0.966261   0.981044
+ 0.0372783  0.0100412
+ 0.899013   0.758491
+ 0.473352   0.334147
+ 0.0438898  0.256301
 ```
 
 ### The nested Archimedean copulas
@@ -285,10 +288,10 @@ Nested_Clayton_cop(Clayton_cop[Clayton_cop(2, 3.0), Clayton_cop(2, 4.0)], 0, 1.0
 Only the nesting within the same family is supported. The sufficient nesting condition requires parameters of the children copulas to be larger than the parameter of the parent copula. For sampling one uses the algorithm form  McNeil, A.J., 'Sampling nested Archimedean copulas', Journal of Statistical Computation and Simulation 78, 567–581 (2008).
 
 ```julia
-julia> a = Clayton_cop(2, 0.9, "Kendall")
+julia> a = Clayton_cop(2, 0.9, KendallCorrelation)
 Clayton_cop(2, 18.000000000000004)
 
-julia> b = Nested_Clayton_cop([a], 1, .2, "Kendall")
+julia> b = Nested_Clayton_cop([a], 1, .2, KendallCorrelation)
 Nested_Clayton_cop(Clayton_cop[Clayton_cop(2, 18.000000000000004)], 1, 0.5)
 
 julia> x = simulate_copula(500000, b);
@@ -337,19 +340,19 @@ julia> simulate_copula(2, gp)
 More straight forward example
 
 ```julia
-julia> a = Gumbel_cop(2, .9, "Kendall")
+julia> a = Gumbel_cop(2, .9, KendallCorrelation)
 Gumbel_cop(2, 10.000000000000002)
 
-julia> b = Gumbel_cop(2, 0.8, "Kendall")
+julia> b = Gumbel_cop(2, 0.8, KendallCorrelation)
 Gumbel_cop(2, 5.000000000000001)
 
-julia> p = Nested_Gumbel_cop([a], 1, 0.6, "Kendall")
+julia> p = Nested_Gumbel_cop([a], 1, 0.6, KendallCorrelation)
 Nested_Gumbel_cop(Gumbel_cop[Gumbel_cop(2, 10.000000000000002)], 1, 2.5)
 
-julia> p1 = Nested_Gumbel_cop([b], 1, 0.5, "Kendall")
+julia> p1 = Nested_Gumbel_cop([b], 1, 0.5, KendallCorrelation)
 Nested_Gumbel_cop(Gumbel_cop[Gumbel_cop(2, 5.000000000000001)], 1, 2.0)
 
-julia> pp = Double_Nested_Gumbel_cop([p,p1], 0.1, "Kendall")
+julia> pp = Double_Nested_Gumbel_cop([p,p1], 0.1, KendallCorrelation)
 Double_Nested_Gumbel_cop(Nested_Gumbel_cop[Nested_Gumbel_cop(Gumbel_cop[Gumbel_cop(2, 10.000000000000002)], 1, 2.5), Nested_Gumbel_cop(Gumbel_cop[Gumbel_cop(2, 5.000000000000001)], 1, 2.0)], 1.1111111111111112)
 
 julia> x = simulate_copula(750_000, pp);
@@ -386,7 +389,7 @@ julia> simulate_copula(3, c)
 ```
 
 ```julia
-julia> c = Hierarchical_Gumbel_cop([.9, 0.7, 0.5, 0.1], "Kendall")
+julia> c = Hierarchical_Gumbel_cop([.9, 0.7, 0.5, 0.1], KendallCorrelation)
 Hierarchical_Gumbel_cop(5, [10.000000000000002, 3.333333333333333, 2.0, 1.1111111111111112])
 
 julia> x = simulate_copula(750_000, c);
@@ -431,7 +434,7 @@ Chain_of_Archimedeans(3, [2.0, 3.0], ["frank", "frank"])
 ```
 
 ```julia
-julia> c = Chain_of_Archimedeans([0.7, 0.5, 0.7], "clayton", "Kendall")
+julia> c = Chain_of_Archimedeans([0.7, 0.5, 0.7], "clayton", KendallCorrelation)
 Chain_of_Archimedeans(4, [4.666666666666666, 2.0, 4.666666666666666], ["clayton", "clayton", "clayton"])
 
 julia> x = simulate_copula(750_000, c);
@@ -447,7 +450,7 @@ julia> corkendall(x)
 Negative correlations are supported here as well:
 
 ```julia
-julia> c = Chain_of_Archimedeans([0.7, 0.5, -0.7], "clayton", "Kendall")
+julia> c = Chain_of_Archimedeans([0.7, 0.5, -0.7], "clayton", KendallCorrelation)
 Chain_of_Archimedeans(4, [4.666666666666666, 2.0, -0.8235294117647058], ["clayton", "clayton", "clayton"])
 
 julia> x = simulate_copula(750_000, c);
@@ -690,6 +693,27 @@ julia> gcop2arch(x, ["clayton" => [1,2]])
   0.154893   0.893253   0.989712
  -0.657297  -0.339814  -1.54419
 
+
+julia> Random.seed!(42);
+
+julia> x = Array(rand(MvNormal(Σ), 6)')
+6×3 Array{Float64,2}:
+-0.556027  -0.662861   -0.384124
+-0.299484   1.38993    -0.571326
+-0.468606  -0.0990787  -2.3464  
+1.00331    1.43902     0.966819
+0.518149   1.55065     0.989712
+-0.886205   0.149748   -1.54419
+
+julia> gcop2arch(x, ["gumbel" => [1,2]])
+6×3 Array{Float64,2}:
+0.178913   1.60797    -0.384124
+0.579476   0.880272   -0.571326
+-0.986662  -0.0180474  -2.3464  
+1.20299    2.55397     0.966819
+0.857086   1.86212     0.989712
+-0.548206  -0.439289   -1.54419
+
 ```
 
 To change the chosen marginals subset list in `ind` of the multivariate Gaussian distributed data `x` by means of the Frechet maximal copula run:

src/DatagenCopulaBased.jl

@@ -37,7 +37,7 @@ module DatagenCopulaBased
   export Nested_Clayton_cop, Nested_AMH_cop, Nested_Frank_cop, Nested_Gumbel_cop
   export Double_Nested_Gumbel_cop, Hierarchical_Gumbel_cop
   export Chain_of_Archimedeans, Chain_of_Frechet
-
+  export SpearmanCorrelation, KendallCorrelation, CorrelationType
   export cormatgen, cormatgen_constant, cormatgen_toeplitz, convertmarg!
   export cormatgen_constant_noised, cormatgen_toeplitz_noised, cormatgen_rand
   export cormatgen_two_constant, cormatgen_two_constant_noised

src/archcopcorrelations.jl

@@ -1,3 +1,11 @@
+# empty types for correlations
+
+abstract type CorrelationType end
+
+struct KendallCorrelation <: CorrelationType end
+struct SpearmanCorrelation <: CorrelationType end
+
+
 """
   Debye(x::Float64, k::Int)
 
@@ -63,13 +71,13 @@ end
 # Spearman ρ to copulas parameter
 
 """
- ρ2θ(ρ::Union{Float64, Int}, copula::String)
+ ρ2θ(ρ::Float64, copula::String)
 
- Returns a Float, an archimedean copula parameter given expected Spermann correlation
+ Returns a Float, an Archimedean copula parameter given expected Spermann correlation
  ρ and a copula.
 
 """
-function ρ2θ(ρ::Union{Float64, Int}, copula::String)
+function ρ2θ(ρ::Float64, copula::String)
   if copula == "gumbel"
     return gumbelρ2θ(ρ)
   elseif copula == "clayton"
@@ -84,15 +92,15 @@ end
 
 ### Clayton and gumbel copulas
 
-function Ccl(x, θ::Union{Int, Float64})
+function Ccl(x, θ::Float64)
   if θ > 0
     return (x[1]^(-θ)+x[2]^(-θ)-1)^(-1/θ)
   else
     return (maximum([x[1]^(-θ)+x[2]^(-θ)-1, 0]))^(-1/θ)
   end
 end
 
-Cg(x, θ::Union{Int, Float64}) = exp(-((-log(x[1]))^θ+(-log(x[2]))^θ)^(1/θ))
+Cg(x, θ::Float64) = exp(-((-log(x[1]))^θ+(-log(x[2]))^θ)^(1/θ))
 
 dilog(x) = quadgk(t -> log(t)/(1-t), 1, x)[1]