2019/01/18 by Alexander E. Litvak, Konstantin Tikhomirov, Litvak, Alexander E. +1
Computer Science · Decision Sciences · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Statistical Distribution Estimation and Applications #math.PR
paper · pdf · doi:10.48550/arxiv.1901.07398
A small observation published in Zapiski Nauchnykh Seminarov POMI, 457 (2017), 265--275. arXiv admin note: substantial text overlap with arXiv:1609.02126
arxiv created 2019/01/18 · openalex publication_date 2019/01/18 · arxiv updated 2019/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let X1, …, Xn be independent non-negative random variables with cumulative distribution functions F1,F2,…,Fn, each satisfying certain (rather mild) conditions. We show that the median of k-th smallest order statistic of the vector (X1, …, Xn) is equivalent to the quantile of order (k-1/2)/n with respect to the averaged distribution F=(1)/(n)∑i=1n Fi.