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ON CHARACTERIZATIONS OF DISTRIBUTIONS BY MEAN

ABSOLUTE DEVIATION AND VARIANCE BOUNDS

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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.

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