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What is Learnable in Valiant's Theory of the Learnable? 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On Stochastic Comparisons of Order Statistics from Heterogeneous Exponential Samples
Yaming Yu · 2016-07-22 · via math.ST updates on arXiv.org

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