Bivariate distributions with equi-dispersed normal conditionals and related models

TL;DR

This paper explores univariate and bivariate models with equi-dispersed normal distributions, discussing their properties, inference methods, and applications, highlighting their place within exponential family distributions.

Contribution

It introduces and analyzes the class of equi-dispersed normal models, emphasizing their distributional features and inferential aspects, which are less studied compared to other equi-dispersed distributions.

Findings

Equi-dispersed normal distributions form a one-parameter exponential family.

Distributional features of univariate and bivariate models are characterized.

An example application demonstrates the practical use of these models.

Abstract

A random variable is equi-dispersed if its mean equals its variance. A Poisson distribution is a classical example of this phenomenon. However, a less well-known fact is that the class of normal densities that are equi-dispersed constitutes a one parameter exponential family. In the present article our main focus is on univariate and bivariate models with equi-dispersed normal component distributions. We discuss distributional features of such models, explore inferential aspects and include an example of application of equi-dispersed models. Some related models are discused in Appendices.