2018/06/13 by Nickos Papadatos, Papadatos, Nickos
Decision Sciences · Engineering · Mathematics · #FOS: Mathematics #Probabilistic and Robust Engineering Design #Reliability and Maintenance Optimization #Statistical Distribution Estimation and Applications #Statistics Theory (math.ST) #math.ST #stat.TH
paper · pdf · doi:10.48550/arxiv.1806.05095
17 pages
arxiv created 2018/06/13 · openalex publication_date 2018/06/13 · arxiv updated 2018/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.