CHARACTERIZATION OF GENERALIZED MIXTURES OF EXPONENTIAL DISTRIBUTION BASED ON CONDITIONAL EXPECTATION OF ORDER STATISTICS

Abstract

Generalized mixtures of exponential random variables (Everitt and Hand (1981) and Johnson et al. (1994)) X₁ and X₂ are identified in terms of their relations between the best predictor of X_2:2 given X_1:2 and the functions of the failure rate (or hazard function) of the distribution. Here X_1:2 and X_2:2 denote the corresponding order statistics. In addition, we also mention some related theorems in order to characterize the generalized mixtures of exponential distribution. Moreover, when the sample size is n, the above results are also valid.