On Stochastic Comparisons of Order Statistics from Heterogeneous Exponential Samples

Abstract

We show that the $k$th order statistic from a heterogeneous sample of $n\ge k$ 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.

arXiv comment8 pages

References in corpus (2)

• Stochastic Ordering of Exponential Family Distributions and Their Mixtures
• On the Unique Crossing Conjecture of Diaconis and Perlman on Convolutions of Gamma Random Variables