The mixtures of Gompertz random variables (Gompertz, 1825) X1 and X2 are identified in terms of relations between the conditional expectation of [exp (αX2:2) — exp (αX1:2)]k given X1:2 and the hazard rate function of the distribution, k is a positive integer and α < 0. Here X1:2 and X2:2 denote the corresponding order statistics. In addition, we also mention some related theorems to characterize the mixtures of Gompertz distributions. Finally, when the sample size is n, the above results are also valid and we also give an application to Multi-Hit models of carcinogenesis (Parallel Systems).
