Further results on the bivariate semi-parametric singular family of distributions

Abstract

General classes of bivariate distributions are well-studied in the literature. Most of these classes are proposed via a copula formulation or extensions of some characterization properties in the univariate case. In Kundu (2022), we see one such semi-parametric family useful to model bivariate data with ties. This model is a general semi-parametric model with a baseline. In this paper, we present a characterization property of this class of distributions in terms of a functional equation. The general solution to this equation is explored. Necessary and sufficient conditions under which the solution becomes a bivariate distribution are investigated. An application of the characterization property of the proposed class for generating bivariate pairs of random variables from a member distribution is also discussed.