Propriétés statistiques des copules de valeurs extrêmes bidimensionnelles

Kilani Ghoudi, Abdelhaq Khoudraji, Louis Paul Rivest

Research output: Contribution to journalArticlepeer-review

84 Citations (Scopus)

Abstract

Let (X,Y) be a bivariate random vector whose distribution function H(x,y) belongs to the class of bivariate extreme-value distributions. If F1 and F2 are the marginals of X and Y, then H(x,y) = C{F1(x),F2(y)}, where C is a bivariate extreme-value dependence function. This paper gives the joint distribution of the random variables Z = {log F1(X)}/{log F1(X)F2(Y)} and W = C{F1(X),F2(Y)}. Using this distribution, an algorithm to generate random variables having bivariate extreme-value distribution is presented. Furthermore, it is shown that for any bivariate extreme-value dependence function C, the distribution of the random variable W = C{ F1(X),F2(Y)} belongs to a monoparametric family of distributions. This property is used to derive goodness-of-fit statistics to determine whether a copula belongs to an extreme-value family.

Original languageEnglish
Pages (from-to)187-197
Number of pages11
JournalCanadian Journal of Statistics
Volume26
Issue number1
DOIs
Publication statusPublished - Mar 1998
Externally publishedYes

Keywords

  • Galambos's distribution
  • Goodness of fit
  • Gumbel's dependence function
  • Jackknife variance estimator
  • Multivariate extreme-value distributions
  • Simulation
  • U-statistic

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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