Optimal moment inequalities for order statistics from nonnegative random variables

TL;DR

This paper derives the tightest upper bounds for moments of order statistics from nonnegative independent variables, including the sample minimum, based on population means, with applications in reliability systems.

Contribution

It provides the best possible upper bounds for moments of order statistics from nonnegative variables, extending to the sample minimum for independent, non-identically distributed variables.

Findings

Established optimal upper bounds for moments of order statistics.

Extended results to the sample minimum for independent, non-identically distributed variables.

Applicable to reliability system analysis.

Abstract

We obtain the best possible upper bounds for the moments of a single order statistic from independent, non-negative 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. Key-words and phrases: order statistics; optimal moment bounds; nonnegative random variables; sample minimum; reliability systems.