Update paper.md

joss/paper.md

@@ -108,36 +108,6 @@ using Turing
   Turing.Turing.@addlogprob! loglikelihood(D, dataset)
 end
 ```
-Outside the common context we can use the API to work on different aspects, suppose you want to generate random samples of a copula whose parameter depends on a covariate $X$ [@abegaz2012], for example, Consider the Frank copula whose parameter depends on a covariate $X$ that follows a truncated normal distribution with mean zero and variance 9. Also, consider the parameter $\theta(x), x \in [-2,2]$.
-```julia
-using Distributions, Copulas, DataFrames
-
-x= truncated(Normal(0,3),-2,2) 
-
-function model_1(x)
-   return (10-1.5x^2)
-end
-
-data = rand(x,10^5)
-
-#Frank Copula whose parameter depends on a covariate
-function rFrank(x, C_function, dimension)
-  data_list = DataFrame(u1=Float64[], u2=Float64[])
-
-  for i in x
-    param = C_function(i)
-    copula_instance = FrankCopula(dimension, param)
-    value_copula = rand(copula_instance, 1)
-    push!(data_list, (value_copula[1], value_copula[2]))
-  end
-
-  return data_list
-end
-
-New_frank = rFrank(data, model_1, 2)
-```
-In this way we easily obtain random samples of a new bivariate Frank copula whose parameter can depend on any covariate.
-
 ## The Archimedean interface
 
 Archimedean copulas form a large class of copulas that has seen a lot of theoretical work. Among others, you may take a look at [@mcneilMultivariateArchimedeanCopulas2009b]. We use [`WilliamsonTransforms.jl`](https://github.com/lrnv/WilliamsonTransforms.jl/)'s implementation of the Williamson $d$-transfrom to sample from any archimedean copula, including for example the `ClaytonCopula` with negative dependence parameter in any dimension, which is a first to our knowledge.