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ON STOCHASTIC COMPARISONS OF ORDER STATISTICS FROM HETEROGENEOUS EXPONENTIAL SAMPLES

Published online by Cambridge University Press:  29 October 2019

Yaming Yu Open the ORCID record for Yaming Yu [Opens in a new window]
Yaming Yu*
Affiliation:
Department of Statistics, University of California, Irvine, CA 92697, USA E-mail: [email protected]
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Abstract

We show that the kth order statistic from a heterogeneous sample of n ≥ k exponential random variables is larger than that from a homogeneous exponential sample in the sense of star ordering, as conjectured by Xu and Balakrishnan [14]. As a consequence, we establish hazard rate ordering for order statistics between heterogeneous and homogeneous exponential samples, resolving an open problem of Pǎltǎnea [11]. Extensions to general spacings are also presented.

Keywords

convolutiondispersive orderingexponential distributionmajorizationstochastic order
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 35 , Issue 3 , July 2021 , pp. 532 - 537
Copyright
© Cambridge University Press 2019

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