A general approach to generate random variates for multivariate copulae
(2018) In Australian & New Zealand Journal of Statistics 60(1). p.140155 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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/3b6530834c9147c1a96ec6d6226adde3
 author
 Tajvidi, Nader ^{LU} and Turlach, Berwin
 organization
 publishing date
 20180314
 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
 WileyBlackwell
 external identifiers

 scopus:85043991512
 ISSN
 1467842X
 DOI
 10.1111/anzs.12209
 language
 English
 LU publication?
 yes
 id
 3b6530834c9147c1a96ec6d6226adde3
 date added to LUP
 20180316 16:01:48
 date last changed
 20201007 05:47:09
@article{3b6530834c9147c1a96ec6d6226adde3, 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 = {1467842X}, language = {eng}, month = {03}, number = {1}, pages = {140155}, publisher = {WileyBlackwell}, 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}, }