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Some concept of Markov property of discrete order statistics arising from independent and non-identically distributed variables

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  • Jasiński, Krzysztof

Abstract

Let X1:n≤⋯≤Xn:n be order statistics related to independent, identically distributed discrete X1,…,Xn. The sequence (Xi:n,T˜i)i=1n exhibits Markovian property, where T˜i=#{j≤i:Xj:n=Xi:n}. We extend this result by considering order statistics from independent and not necessarily identically distributed discrete random variables.

Suggested Citation

  • Jasiński, Krzysztof, 2020. "Some concept of Markov property of discrete order statistics arising from independent and non-identically distributed variables," Statistics & Probability Letters, Elsevier, vol. 160(C).
    • Handle: RePEc:eee:stapro:v:160:y:2020:i:c:s0167715220300213
    DOI: 10.1016/j.spl.2020.108718
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    References listed on IDEAS

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    1. Davies, Katherine & Dembińska, Anna, 2019. "On the number of failed components in a k-out-of-n system upon system failure when the lifetimes are discretely distributed," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 47-61.
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