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

Article type: Research Article

Authors: Vasudevan, Durga^* | Asha, G.

Affiliations: Department of Statistics, Cochin University of Science and Technology, Cochin, Kerala, India

Correspondence: [*] Corresponding author: Durga Vasudevan, Department of Statistics, Cochin University of Science and Technology, Cochin, Kerala 682022, India. Tel.: +91 9947133870; E-mail: [email protected].

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.

Keywords: Bivariate distributions, functional equation, proportional hazard models, semi-parametric class

DOI: 10.3233/MAS-231436

Journal: Model Assisted Statistics and Applications, vol. 18, no. 4, pp. 311-320, 2023