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A general approach to generate random variates for multivariate copulae

Tajvidi, Nader LU and Turlach, Berwin (2018) In Australian & New Zealand Journal of Statistics 60(1). p.140-155
Abstract
We suggest two methods for simulating from a multivariate copula in an arbitrary dimension. Although our main emphasis in this paper is on multivariate extreme value distributions, the proposed methods can be applied to any copula. The basic idea is to approximate the (unknown) density of the copula by a distribution that has a piece‐wise constant (histogram) density. This is achieved by partitioning the support of a given copula C into a large number of hyper‐rectangles and using them to generate random variates from an approximation of the copula. We suggest two methods for finding this approximation which correspond to either finding hyper‐rectangles which have equal probability mass with respect to C, or determining a partition using... (More)
We suggest two methods for simulating from a multivariate copula in an arbitrary dimension. Although our main emphasis in this paper is on multivariate extreme value distributions, the proposed methods can be applied to any copula. The basic idea is to approximate the (unknown) density of the copula by a distribution that has a piece‐wise constant (histogram) density. This is achieved by partitioning the support of a given copula C into a large number of hyper‐rectangles and using them to generate random variates from an approximation of the copula. We suggest two methods for finding this approximation which correspond to either finding hyper‐rectangles which have equal probability mass with respect to C, or determining a partition using hyper‐squares of equal volume and finding the corresponding probability mass of each hyper‐square. We also discuss how the generated random variates can be used as proposals in a Metropolis–Hastings algorithm, when C is an absolutely continuous distribution function, to generate a sequence of random variates from C. An implementation of the proposed methodologies is provided for the statistical computing and graphics environment R in our package called SimCop. (Less)
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author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
copula, extreme value distributions, Hastings algorithm, Metropolis, random variate generation
in
Australian & New Zealand Journal of Statistics
volume
60
issue
1
pages
16 pages
publisher
Wiley-Blackwell
external identifiers
  • scopus:85043991512
ISSN
1467-842X
DOI
10.1111/anzs.12209
language
English
LU publication?
yes
id
3b653083-4c91-47c1-a96e-c6d6226adde3
date added to LUP
2018-03-16 16:01:48
date last changed
2020-10-07 05:47:09
@article{3b653083-4c91-47c1-a96e-c6d6226adde3,
  abstract     = {We suggest two methods for simulating from a multivariate copula in an arbitrary dimension. Although our main emphasis in this paper is on multivariate extreme value distributions, the proposed methods can be applied to any copula. The basic idea is to approximate the (unknown) density of the copula by a distribution that has a piece‐wise constant (histogram) density. This is achieved by partitioning the support of a given copula C into a large number of hyper‐rectangles and using them to generate random variates from an approximation of the copula. We suggest two methods for finding this approximation which correspond to either finding hyper‐rectangles which have equal probability mass with respect to C, or determining a partition using hyper‐squares of equal volume and finding the corresponding probability mass of each hyper‐square. We also discuss how the generated random variates can be used as proposals in a Metropolis–Hastings algorithm, when C is an absolutely continuous distribution function, to generate a sequence of random variates from C. An implementation of the proposed methodologies is provided for the statistical computing and graphics environment R in our package called SimCop.},
  author       = {Tajvidi, Nader and Turlach, Berwin},
  issn         = {1467-842X},
  language     = {eng},
  month        = {03},
  number       = {1},
  pages        = {140--155},
  publisher    = {Wiley-Blackwell},
  series       = {Australian & New Zealand Journal of Statistics},
  title        = {A general approach to generate random variates for multivariate copulae},
  url          = {http://dx.doi.org/10.1111/anzs.12209},
  doi          = {10.1111/anzs.12209},
  volume       = {60},
  year         = {2018},
}