Exact Distribution of Random Order Statistics and Applications in Risk Management

Vasileios M. Koutras () and Markos V. Koutras ()
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Vasileios M. Koutras: University of Piraeus
Markos V. Koutras: University of Piraeus

Methodology and Computing in Applied Probability, 2020, vol. 22, issue 4, 1539-1558

Abstract: 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).

Keywords: Bernoulli mixtures; Non-performing loans; Panjer family; Phase-type distributions; Power series distributions; Random order statistics; Risk management; Samples of random size; 62E15; 62G30; 60J10 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11009-018-9662-z

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