On characterizations of distributions by mean absolute deviation and variance bounds |
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Authors: | R. M. Korwar |
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Affiliation: | (1) Department of Mathematics and Statistics, University of Massachusetts, 01003 Amherst, MA, U.S.A. |
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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. |
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Keywords: | Characterizations geometric hypergeometric and Pearson distributions mean absolute deviation mixtures |
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