IDENTIFICATION OF MIXTURES OF EXPONENTIAL DISTRIBUTIONS BY MEANS OF A PREDICTOR AND EXPECTATIONS OF ORDER STATISTICS

Abstract

Discrete mixtures of exponential random variables X₁ and X₂ are identified in terms of (i) relations between the best predictor of max (X₁, X₂) given min (X₁, X₂) and the failure rate of the distribution, and (ii) relations between conditional expectation of some appropriate functions of order statistics on some others and the failure rate of the distribution.