Bivariate distributions with equi-dispersed normal conditionals and related models

Barry C. Arnold () and B. G. Manjunath ()
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Barry C. Arnold: University of California
B. G. Manjunath: University of Hyderabad

Metrika: International Journal for Theoretical and Applied Statistics, 2024, vol. 87, issue 4, No 4, 427-448

Abstract: 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.

Keywords: Equi-dispersed; Normal conditionals; Exponential family; Maximum likelihood estimators; Pseudo likelihood (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00184-023-00921-5

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