A Continuous Bivariate Exponential Distribution
Abstract Among many bivariate exponential distributions proposed in the statistical literature, the BVE of Marshall and Olkin (1967) is widely accepted. An important property of the BVE is that if X and Y are BVE, then X = Y with positive probability, which makes the BVE inappropriate in many practical situations. For example, in certain types of diseases where the occurrence of simultaneous failure of a pair of organs is rare, an appropriate bivariate exponential distribution to describe the failure of these paired organs should be one that is absolutely continuous. The BVE, however, possesses some other properties that have useful physical interpretations. Therefore, the derivation of an absolutely continuous bivariate exponential distribution retaining the desirable properties of the BVE appears to be a worthwhile objective. To this end, we consider a characterization property of the BVE and modify it suitably to derive an absolutely continuous bivariate distribution. The important characterization pro...