We introduce a comprehensive method for establishing stochastic orders among order statistics in the independent and identically distributed 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. Moreover, for convex-ordered families, we show that an application of Jensen’s inequality gives bounds for the probability that a random variable exceeds the expected value of its corresponding order statistic.

(2025). Inequalities and bounds for expected order statistics from transform-ordered families [journal article - articolo]. In JOURNAL OF APPLIED PROBABILITY. Retrieved from https://hdl.handle.net/10446/299848

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

Lando, Tommaso;
2025-04-08

Abstract

We introduce a comprehensive method for establishing stochastic orders among order statistics in the independent and identically distributed 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. Moreover, for convex-ordered families, we show that an application of Jensen’s inequality gives bounds for the probability that a random variable exceeds the expected value of its corresponding order statistic.
articolo
8-apr-2025
Arab, Idir; Lando, Tommaso; Oliveira, Paulo Eduardo
(2025). Inequalities and bounds for expected order statistics from transform-ordered families [journal article - articolo]. In JOURNAL OF APPLIED PROBABILITY. Retrieved from https://hdl.handle.net/10446/299848
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