Maximum Likelihood Estimation and Hypothesis Testing in the Bivariate Exponential Model of Marshall and Olkin.

The present work concerns statistical inference in the bivariate exponential distribution introduced by Marshall and Olkin. Even though the distribution has a singular component, the use of a special dominating measure leads to an explicit form of the likelihood whose properties are investigated. The existence, uniqueness and asymptotic distributional properties of the maximum likelihood estimators are studied. Using the criterion of generalized variance, it is shown that the simple unbiased estimators proposed by Arnold are asymptotically less efficient than the maximum likelihood estimators and the loss in efficiency is particularly serious in the case of independence. Uniformly most powerful test for independence is derived for the special model having identical marginal distributions.