A bivariate compound class of geometric–Poisson and lifetime distributions

Recently, Alkarni and Oraby (2012) obtained general forms for some properties of the compound class of Poisson and lifetime (PL) distributions. In this paper, we obtain some general forms for joint density, cumulative distribution, and survival functions of the bivariate case of PL class. Its conditional distributions are also studied. In addition, the compound class of geometric and lifetime distributions as well as its mixed bivariate case are discussed. For this class some conditional probabilities useful for reliability, biological survey, and engineering are also studied. Our class contains several new mixed bivariate distributions in special cases.