Inequalities and bounds for expected order statistics from transform-ordered families

Tommaso Lando Idir Arab; Paulo Eduardo Oliveira

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arXiv · 2403.03802

Inequalities and bounds for expected order statistics from transform-ordered families

Tommaso Lando Idir Arab·Paulo Eduardo Oliveira

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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.

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Tommaso Lando Idir Arab, Paulo Eduardo Oliveira. 2024-11-21. Inequalities and bounds for expected order statistics from transform-ordered families. https://arxiv.org/abs/2403.03802

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