Exact range of the parameter of an n-variate FGM copula under homogeneous dependence structure

Abstract

An n-variate Farlie-Gumbel-Morgenstern (FGM) copula consists of 2ⁿ - n - 1 parameters that express multivariate dependence among random variables. Motivated by the dependence structure of the n-variate FGM copula, we derive the exact range of the n-variate FGM copula's parameter. The exact range of the parameter is given by a closedform expression under the condition that all parameters take the same value. Moreover, under the same condition, we reveal that the n-variate FGM copula becomes the independence copula for n → ∞. This result contributes to the dependence modeling such as reliability analysis considering dependent failure occurrence.