Random number generation for nested Archimedean copulas (of class
outer_nacopula, specifically), aka
sampling nested Archimedean copulas will generate
random vectors of dimension d (=
integer specifying the sample size, that is, the number of copula-distributed random vectors U_i, to be generated.
an R object of
only for back compatibility: former name of
possibly further arguments for the given copula family.
The generation happens by calling
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).
numeric matrix containing the generated vectors of
random variates from the nested Archimedean copula object
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.
Further, those of the Archimedean families, for example,
1 2 3 4 5 6 7 8 9 10 11 12 13 14
## 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)
Nested Archimedean copula ("outer_nacopula" of dim. 3), with slot 'comp' = (1) and root 'copula' = Archimedean copula ("acopula"), family "Clayton", theta= (0.5) and 1 child copula Nested Archimedean copula ("nacopula"), with slot 'comp' = (2, 3) and root 'copula' = Archimedean copula ("acopula"), family "Clayton", theta= (2) and *no* child copulas
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