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Exact Distribution of Random Order Statistics and Applications in Risk Management

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Abstract

In the present work we study the exact distribution of order statistics coming from a sample of random variables (r.v.’s), with random sample size. Some new results are provided for the exact distribution of the r −th largest observation of the sample, and several interesting properties are developed when the sample size belongs to wide classes of discrete distributions such as the family of power series distributions, the Panjer Family, the class of exchangeable Bernoulli mixtures and the family of Phase-Type distributions. Finally, we illustrate how the stochastic model under study could be exploited for modeling problems arising in financial risk management (monitoring of non-performing loans and insurance portfolio surveillance).

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Acknowledgments

Work funded by National Matching Funds 2016-2017 of the Greek Government, and more specifically by the General Secretariat for Research and Technology (GSRT), related to EU project “ISMPH: Inference for a Semi-Markov Process” (GA No 329128).

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Authors and Affiliations

  1. Department of Statistics and Insurance Science, School of Finance and Statistics, University of Piraeus, Piraeus, Greece

    Vasileios M. Koutras & Markos V. Koutras

Authors
  1. Vasileios M. Koutras
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  2. Markos V. Koutras
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Correspondence to Vasileios M. Koutras.

Additional information

Work done while VMK was a postgraduate student at the Department of Statistics and Insurance Science, Greece

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Koutras, V.M., Koutras, M.V. Exact Distribution of Random Order Statistics and Applications in Risk Management. Methodol Comput Appl Probab 22, 1539–1558 (2020). https://doi.org/10.1007/s11009-018-9662-z

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  • DOI: https://doi.org/10.1007/s11009-018-9662-z

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