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Characterization of discrete populations through conditional expectations of order statistics

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Abstract

In this paper we give some properties of the expected values of any order statistic when one of its adjacent order statistics is known (order mean function) from a sequence of sizen of independent and identically distributed random variables with discrete distribution. Furthermore, we obtain the explicit expressions of the distribution from these order mean functions, and finally, we show the necessary and sufficient conditions for any real function to be an order mean function. We also add some examples of characterization of discrete distributions from the order mean functions.

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Authors and Affiliations

  1. Departmento de Estadística e I. O., Universidad de Murcia, Apdo. 4021, E-30071, Espinado, Murcia, Spain

    Manuel Franco & José M. Ruiz

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  1. Manuel Franco
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  2. José M. Ruiz
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Partially supported by Consejería de Cultura y Educación (C.A.R.M.), under Grant PIB 95/90.

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Franco, M., Ruiz, J.M. Characterization of discrete populations through conditional expectations of order statistics. Statistical Papers 39, 249–262 (1998). https://doi.org/10.1007/BF02929702

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