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Some characterization results based on the conditional expectation of a function of non-adjacent order statistic (record value)

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Abstract

In this paper, we attempt to characterize a distribution by means ofE[ψ(X k +s:n)|X k:n =z]g(z), under some mild conditions on ψ(·) andg(·). An explicit result is provided in the case ofs=1 and a uniqueness result is proved in the case ofs=2. For the general case, an expression is provided for the conditional expectation. Similar results are proved for the record values, both in the continuous as well as in the discrete case (weak records).

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Maine, 04469-5752, Orono, ME, USA

    Ramesh C. Gupta

  2. Department of Management Sciences, Rider University, 08648-3099, Lawrenceville, NJ, USA

    Mohammad Ahsanullah

Authors
  1. Ramesh C. Gupta
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  2. Mohammad Ahsanullah
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Gupta, R.C., Ahsanullah, M. Some characterization results based on the conditional expectation of a function of non-adjacent order statistic (record value). Ann Inst Stat Math 56, 721–732 (2004). https://doi.org/10.1007/BF02506485

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  • DOI: https://doi.org/10.1007/BF02506485

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