Inequalities and bounds for expected order statistics from transform-ordered families
Methodology
2024-11-22 v2
Abstract
We introduce a comprehensive method for establishing stochastic orders among order statistics in the i.i.d. case. This approach relies on the assumption that the underlying distribution is linked to a reference distribution through a transform order. Notably, this method exhibits broad applicability, particularly since several well-known nonparametric distribution families can be defined using relevant transform orders, including the convex and the star transform orders. In the context of convex-ordered families, we demonstrate that applying Jensen's inequality enables the derivation of bounds for the probability that a random variable exceeds the expected value of its corresponding order statistic.
Cite
@article{arxiv.2403.03802,
title = {Inequalities and bounds for expected order statistics from transform-ordered families},
author = {Tommaso Lando Idir Arab and Paulo Eduardo Oliveira},
journal= {arXiv preprint arXiv:2403.03802},
year = {2024}
}