Maximum Likelihood Analysis for Bivariate Exponential Distributions

Abstract

A generalization of Marshall-Olkin(1967) bivariate exponential model is proposed and the existence, uniqueness and asymptotic distributional properties of the maximum likelihood estimators are studied. The classical Marshall- Olkin model is a mixture of an absolutely continuous and a singular component, that concentrates its mass on the line x = y. In this paper, I generalize Marshall-Olkin s results considering a distribution with positive mass on the line x = \mu y, \mu > 0. Some simulation results to compare the two models are presented. I also derive an extension of Marshall-Olkin (1967) model for any function which is continuous and twice continuously differentiable in some open dense domain. This extension gives class of models some of it have exponential marginals. I derive its asymptotic normalities. I model the first mixed moments of bivariate exponential models whose marginals are also exponential using the method of generalized linear models.