Further Results on the Bivariate Semi-parametric Singular Family of Distributions

12/27/2022

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by   Durga Vasudevan, et al.

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General classes of bivariate distributions are well studied in literature. Most of these classes are proposed via a copula formulation or extensions of some characterisation 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 characterisation 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 is investigated.