Inequalities and bounds for expected order statistics from transform-ordered families
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909397898231808 |
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| author | Arab, Tommaso Lando Idir Oliveira, Paulo Eduardo |
| author_facet | Arab, Tommaso Lando Idir Oliveira, Paulo Eduardo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_03802 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Inequalities and bounds for expected order statistics from transform-ordered families Arab, Tommaso Lando Idir Oliveira, Paulo Eduardo Methodology 60E15, 62G30, 62G15 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. |
| title | Inequalities and bounds for expected order statistics from transform-ordered families |
| topic | Methodology 60E15, 62G30, 62G15 |
| url | https://arxiv.org/abs/2403.03802 |