Order Statistics of Independent Samples

Abstract

Bounds for expectations of order statistics from general i.i.d. samples, due to Moriguti [58], are presented in Section 4.1. Bounds of Sections 4.2 and 4.4 for populations with decreasing density and failure rate, and symmetric uni-modal ones, were obtained by Gajek and Rychlik [33]. Results of Section 4.3 for restricted families determined by the star order come from Rychlik [89]. Section 4.5, partially based on Okolewski and Rychlik [65], is devoted to the study of quantile estimation bias in various nonparametric families of distributions.