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

  • Carles M. Cuadras Department of statistics, Faculty of Biology, University of Barcelona, Barcelona, Spain
  • Walter Díaz Department of Mathematics, Faculty of Economics, University of Antioquia, Medellin, Colombia
Keywords: Farlie–Gumbel–Morgenstern distribution, bivariate copulas, stochastic dependence, Pearson contingency coefficient,, dimension of a distribution


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.


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