# rnchild: Sampling Child 'nacopula's In copula: Multivariate Dependence with Copulas

## Description

Method for generating vectors of random numbers of nested Archimedean copulas which are child copulas.

## Usage

 `1` ```rnchild(x, theta0, V0, ...) ```

## Arguments

 `x` an `"nacopula"` object, typically emerging from an `"outer_nacopula"` object constructed with `onacopula()`. `theta0` the parameter (vector) of the parent Archimedean copula which contains `x` as a child. `V0` a `numeric` vector of realizations of V0 following F0 whose length determines the number of generated vectors, that is, for each realization V0, a vector of variates from `x` is generated. `...` possibly further arguments for the given copula family.

## Details

The generation is done recursively, descending the tree implied by the nested Archimedean structure. The algorithm is based on a mixture representation and requires sampling V01 ~ F01 given random variates V0 ~ F0. Calling `"rnchild"` is only intended for experts. The typical call of this function takes place through `rnacopula()`.

## Value

a list with components

 `U` a `numeric` matrix containing the vector of random variates from the child copula. The number of rows of this matrix therefore equals the length of V0 and the number of columns corresponds to the dimension of the child copula. `indcol` an `integer` vector of indices of `U` (the vector following a nested Archimedean copula of which `x` is a child) whose corresponding components of `U` are arguments of the nested Archimedean copula `x`.

`rnacopula`, also for the references. Further, classes `"nacopula"` and `"outer_nacopula"`; see also `onacopula()`.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21``` ```## Construct a three-dimensional nested Clayton copula with parameters ## chosen such that the Kendall's tau of the respective bivariate margins ## are 0.2 and 0.5. theta0 <- copClayton@iTau(.2) theta1 <- copClayton@iTau(.5) C3 <- onacopula("C", C(theta0, 1, C(theta1, c(2,3)))) ## Sample n random variates V0 ~ F0 (a Gamma(1/theta0,1) distribution) n <- 1000 V0 <- copClayton@V0(n, theta0) ## Given these variates V0, sample the child copula, that is, the bivariate ## nested Clayton copula with parameter theta1 U23 <- rnchild(C3@childCops[[1]], theta0, V0) ## Now build the three-dimensional vectors of random variates by hand U1 <- copClayton@psi(rexp(n)/V0, theta0) U <- cbind(U1, U23\$U) ## Plot the vectors of random variates from the three-dimensional nested ## Clayton copula splom2(U) ```