Another generalization of the bivariate FGM distribution with two-dimensional extensions

Abstract

The Farlie–Gumbel–Morgenstern family of bivariate distributions with given marginals is frequently used in theory and applications and has been generalized in many ways. With the help of two auxiliary distributions, we propose another generalization and study its properties. After defining the dimension of a distribution as the cardinal of the set of canonical correlations, we prove that some well-known distributions are practically two-dimensional. Then we introduce an extended FGM family in two dimensions and study how to approximate any distribution to this family.