R: Sampling Nested Archimedean Copulas

rnacopula {copula} | R Documentation

## Sampling Nested Archimedean Copulas

### Description

Random number generation for nested Archimedean copulas (of class `outer_nacopula`, specifically), aka sampling nested Archimedean copulas will generate `n` random vectors of dimension d (= `dim(x)`).

### Usage

    rnacopula(n, copula, x, ...)

### Arguments

`n` | integer specifying the sample size, that is, the number of copula-distributed random vectors U_i, to be generated.
`copula` | an R object of `class` `"outer_nacopula"`, typically from `onacopula()`.
`x` | only for back compatibility: former name of `copula` argument.
`...` | possibly further arguments for the given copula family.

### Details

The generation happens by calling `rnchild()` on each child copula (which itself recursively descends the tree implied by the nested Archimedean structure). The algorithm is based on a mixture representation of the generic distribution functions F0 and F01 and is presented in McNeil (2008) and Hofert (2011a). Details about how to efficiently sample the distribution functions F0 and F01 can be found in Hofert (2010), Hofert (2012), and Hofert and Mächler (2011).

### Value

`numeric` matrix containing the generated vectors of random variates from the nested Archimedean copula object `copula`.

### References

McNeil, A. J. (2008). Sampling nested Archimedean copulas. Journal of Statistical Computation and Simulation 78, 6, 567–581.

Hofert, M. (2010). Efficiently sampling nested Archimedean copulas. Computational Statistics & Data Analysis 55, 57–70.

Hofert, M. (2012), A stochastic representation and sampling algorithm for nested Archimedean copulas. Journal of Statistical Computation and Simulation, 82, 9, 1239–1255.

Hofert, M. (2012). Sampling exponentially tilted stable distributions. ACM Transactions on Modeling and Computer Simulation 22, 1 (3rd article).

Hofert, M. and Mächler, M. (2011). Nested Archimedean Copulas Meet R: The nacopula Package. Journal of Statistical Software 39, 9, 1–20.

### See Also

`rnchild`; classes `"nacopula"` and `"outer_nacopula"`; see also `onacopula()`. `rnacModel` creates random nacopula models, i.e., the input `copula` for `rnacopula(n, copula)`.

Further, those of the Archimedean families, for example, `copGumbel`.

### Examples

    ## 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 :
    C3 <- onacopula("C", C(copClayton@iTau(0.2), 1,
                           C(copClayton@iTau(0.5), c(2,3))))
    C3

    ## Sample n vectors of random variates from this copula.  This involves
    ## sampling exponentially tilted stable distributions
    n <- 1000
    U <- rnacopula(n, C3)

    ## Plot the drawn vectors of random variates
    splom2(U)

[Package copula version 1.0-1 Index]