stash stuff out

src/Generator/FrailtyGenerator.jl

@@ -0,0 +1,38 @@
+"""
+    FrailtyGenerator{TX}
+
+Fields:
+* `X::TX` -- a random variable that represents the frailty distribution.
+
+Constructor
+
+    FrailtyGenerator(X::Distributions.UnivariateDistribution)
+
+The `FrailtyGenerator` allows to construct a completely monotonous archimedean generator from a positive random variable `X::Distributions.UnivariateDistribution`, assuming the distribution has a completely monotonous laplace transform (which will be used as the generator).
+
+References: 
+* [williamson1955multiply](@cite) Williamson, R. E. (1956). Multiply monotone functions and their Laplace transforms. Duke Math. J. 23 189–207. MR0077581
+* [mcneil2009](@cite) McNeil, Alexander J., and Johanna Nešlehová. "Multivariate Archimedean copulas, d-monotone functions and ℓ 1-norm symmetric distributions." (2009): 3059-3097.
+* [mcneil2008](@cite) M
+"""
+struct FrailtyGenerator{TX} <: Generator
+    X::TX
+    function FrailtyGenerator(X)
+        # Check that the laplace transfrom is implemented ? 
+        # it can be through `mgf`, `cgf = log(mgf)` or `cf`. 
+        # the link is `mgf(t) = cf(- im * t)`
+
+        # What we want here is that laplac tranfrom, that is `mgf(-t)` or thus `real(cf(im * t))`.
+
+        # the only condition is that the support of the R.V is positive according to 
+
+        # Check that X is indeed a positively supported random variable ?
+
+        # Other conditions ? We should do a thorough check here. 
+        return new{typeof(X)}(X)
+    end
+end
+max_monotony(::FrailtyGenerator) = Inf
+ϕ(G::FrailtyGenerator, t) = Distributions.mgf(G.X,t)
+williamson_dist(G::FrailtyGenerator, d) = WilliamsonFromFrailty(G.X,d)
+

src/UnivariateDistribution/WilliamsonFromFrailty.jl

@@ -10,14 +10,12 @@ function Distributions.rand(rng::Distributions.AbstractRNG, D::WilliamsonFromFra
     return sy/f
 end
 function Distributions.cdf(D::WilliamsonFromFrailty{TF,d}, x::Real) where {TF,d}
-    # how to compute this cdf ? 
     return 1 - Distributions.expectation(
         e -> Distributions.cdf(D.frailty_dist,e/x),
         Distributions.Erlang(d)
     )
 end
 function Distributions.pdf(D::WilliamsonFromFrailty{TF,d}, x::Real) where {TF,d}
-    # how to compute this cdf ? 
     return 1/x^2 * Distributions.expectation(
         e -> Distributions.pdf(D.frailty_dist,e/x),
         Distributions.Erlang(d)