Bivariate distributions with equi-dispersed normal conditionals and related models

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...

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Bibliographic Details
Published in:Metrika 2024-05, Vol.87 (4), p.427-448
Main Authors: Arnold, Barry C., Manjunath, B. G.
Format: Article
Language:English
Subjects:
Bivariate analysis
Economic Theory/Quantitative Economics/Mathematical Methods
Mathematics and Statistics
Poisson distribution
Probability Theory and Stochastic Processes
Random variables
Statistics
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Summary: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.
ISSN:0026-1335
1435-926X
DOI:10.1007/s00184-023-00921-5