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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Korwar, R.M. On characterizations of distributions by mean absolute deviation and variance bounds. Ann Inst Stat Math 43, 287–295 (1991). https://doi.org/10.1007/BF00118636
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DOI: https://doi.org/10.1007/BF00118636