Characterization of Mixtures of Weibull and Pareto Distributions Based on Conditional Expectation of Order Statistics

摘要

The mixture of Weibull random variables X_1 and X_2 are identified in terms of relations between the conditional expectation of (X_(2∶2)~a - X_(1∶2)~a)~r given X_(1∶2) (or ((X_(2∶2)~a)~k given X_(1∶2),Vk≤ r) and hazard rate function of the distribution, where X_(1∶2) and X_(2∶2) denote the corresponding order statistics, r is a positive integer and a ＞ 0. In addition, by using the natural logarithm transformation, we also characterize and mixture of Pareto distributions based on the conditional expectation of order statistics. Furthermore, 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). Finally, we also characterize mixture of Weibull and Pareto distributions based on the conditional expectation of upper record values.