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

Bivariate distributions with equi-dispersed normal conditionals and related models