Stochastic representation of FGM copulas using multivariate Bernoulli random variables

Christopher Blier-Wong, Hélène Cossette and Etienne Marceau

Computational Statistics & Data Analysis, 2022, vol. 173, issue C

Abstract: A one-to-one correspondence between Fréchet's class of multivariate Bernoulli distribution with symmetric marginals and the well-known family of Farlie-Gumbel-Morgenstern (FGM) copulas is established. A new stochastic representation of the family of d-variate FGM copulas is introduced. The representation is bijective: from any d-variate Bernoulli distribution, one may define a corresponding d-variate FGM copula; and for any d-variate FGM copula, one finds the corresponding d-variate Bernoulli distribution. The proposed stochastic representation has many advantages, notably establishing stochastic orders, constructing subclasses of FGM copulas and sampling. In particular, one may use the stochastic representation to develop computational methods to perform sampling from subclasses of FGM copulas, which scale well to large dimensions.

Keywords: Multivariate Farlie-Gumbel-Morgenstern copulas; Multivariate Bernoulli distributions; Stochastic representation; Stochastic simulation; Dependence ordering (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:173:y:2022:i:c:s016794732200086x

DOI: 10.1016/j.csda.2022.107506

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