On a Test of Independence in a Bivariate Exponential Distribution

Abstract

The problem of testing independence in the bivariate exponential distribution of Marshall and Olkin is considered here with the assumption of identical marginal distributions. It is shown that in spite of the presence of a nuisance parameter, a uniformly most powerful test exists. The test turns out to be the same as the one proposed by Bernis, et al. , on a heuristic basis. In addition to demonstrating the optimality property of the test, an easily computable expression is provided for the exact power function.