ON CHARACTERIZATIONS OF DISTRIBUTIONS BY MEAN ABSOLUTE DEVIATION AND VARIANCE BOUNDS

R. M. KORWAR

Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003, U.S.A.

(Received October 2, 1989; revised March 24, 1990)

Abstract. In this paper we present a bound for the mean absolute deviation of an arbitrary real-valued function of a discrete random variable. Using this bound we characterize a mixture of two Waring (hence geometric) distributions by linearity of a function involved in the bound. A double Lomax distribution is characterized by linearity of the same function involved in the analogous bound for a continuous distribution. Finally, we characterize the Pearson system of distributions and the generalized hypergeometric distributions by a quadratic function involved in a similar bound for the variance of a function of a random variable.

Key words and phrases: Characterizations, geometric, hypergeometric and Pearson distributions, mean absolute deviation, mixtures.