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OPTIMAL MOMENT INEQUALITIES FOR ORDER STATISTICS FROM NONNEGATIVE RANDOM VARIABLES

Published online by Cambridge University Press:  05 July 2019

Nickos Papadatos Open the ORCID record for Nickos Papadatos [Opens in a new window]
Nickos Papadatos*
Affiliation:
Department of Mathematics, National and Kapodistrian University of Athens, Panepistemiopolis, 157 84 Athens, Greece E-mail: npapadat@math.uoa.gr
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Abstract

We obtain the best possible upper bounds for the moments of a single-order statistic from independent, nonnegative random variables, in terms of the population mean. The main result covers the independent identically distributed case. Furthermore, the case of the sample minimum for merely independent (not necessarily identically distributed) random variables is treated in detail.

Keywords

nonnegative random variablesoptimal moment boundsorder statisticsreliability systemssample minimum
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 35 , Issue 2 , April 2021 , pp. 316 - 330
Copyright
Copyright © Cambridge University Press 2019

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