Bivariate q-extended Weibull morgenstern family and correlation coefficient formulas for some of its sub-models

Abstract

A bivariate extension of a flexible univariate family is proposed. The new family is called bivariate q-extended Weibull Morgenstern family of distributions which can be constructed based on the Farlie-Gumbel-Morgenstern (FGM) copula technique. After introducing the new family, four sub-models are discussed in detail from the theoretical and numerical coefficient of correlation point of view with pointing to the effect of the $ q $ parameter.