On a Poisson Generalized Lindley Distribution: Related Models and Bivariate Extensions

Accepted - January 2025

Abstract

In this paper we demonstrate that univariate and bivariate Poisson generalized Lindley (PGL) distributions can be derived by the different procedures of mixing, generalizing and addition of random variables. We also introduce and study a univariate PGL 6 distribution which is over-dispersed and appears as marginal distribution in three bivariate PGL models, indicating potential use of the corresponding bivariate models to describe correlated count data. Furthermore, we derive two bivariate PGL distributions and examine a variety of their properties including various recurrences, conditional distributions and regression functions. Applications to two bivariate sets of automobile insurance count data are also included.