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Optimal moment inequalities for order statistics from nonnegative random variables (1806.05095v1)
Published 13 Jun 2018 in math.ST and stat.TH
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.