CHARACTERIZATION OF MIXTURES OF GEOMETRIC DISTRIBUTIONS BY MEANS OF A PREDICTOR AND EXPECTATIONS OF ORDER STATISTICS

Abstract

Discrete mixtures of geometric random variables X₁ and X₂ are characterized 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 distributions. The characterizing relations were motivated by the work of Kirmani and Alam (1980) and Dallas (1987).