Exponential order statistics and some combinatorial identities

Palaniappan Vellaisamy and Aklilu Zeleke

Communications in Statistics - Theory and Methods, 2019, vol. 48, issue 20, 5099-5105

Abstract: It is known that the k-th (1≤k≤n) order statistic from the unit exponential distribution can be represented as a sum of independent exponential random variables. We present a proof of this result based on Laplace transform. Also, computing the Laplace transform of the k-th order statistic in two different ways and equating them, we derive several interesting combinatorial identities. A probabilistic interpretation of these identities and their generalizations are also given.

Date: 2019
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DOI: 10.1080/03610926.2018.1508710

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