On Stochastic Comparisons of Order Statistics from Heterogeneous Exponential Samples

2016/07/22 by Yaming Yu, Yu, Yaming
Decision Sciences · Mathematics · #FOS: Mathematics #Probability and Risk Models #Statistical Distribution Estimation and Applications #Statistical Methods and Bayesian Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1607.06564

openalex publication_date 2016/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the kth order statistic from a heterogeneous sample of n≥ k exponential random variables is larger than that from a homogeneous exponential sample in the sense of star ordering, as conjectured by Xu and Balakrishnan (2012). As a consequence, we establish hazard rate ordering for order statistics between heterogeneous and homogeneous exponential samples, resolving an open problem of Pǎltǎnea (2008). Extensions to general spacings are also presented.

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