An easily verifiable dispersion order for discrete distributions
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908639771492352 |
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| author | Eberl, Andreas Klar, Bernhard Suárez-Llorens, Alfonso |
| author_facet | Eberl, Andreas Klar, Bernhard Suárez-Llorens, Alfonso |
| contents | Dispersion is a fundamental concept in statistics, yet standard approaches - especially via stochastic orders - face limitations in the discrete setting. In particular, the classical dispersive order, well-established for continuous distributions, becomes overly restrictive for discrete random variables due to support inclusion requirements. To address this, we propose a novel weak dispersive order for discrete distributions. This order retains desirable properties while relaxing structural constraints, thereby broadening applicability. We further introduce a class of variability measures based on probability concentration, offering robust and interpretable alternatives that conform to classical axioms. Empirical illustrations highlight the practical relevance of this framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_23677 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An easily verifiable dispersion order for discrete distributions Eberl, Andreas Klar, Bernhard Suárez-Llorens, Alfonso Methodology Statistics Theory Dispersion is a fundamental concept in statistics, yet standard approaches - especially via stochastic orders - face limitations in the discrete setting. In particular, the classical dispersive order, well-established for continuous distributions, becomes overly restrictive for discrete random variables due to support inclusion requirements. To address this, we propose a novel weak dispersive order for discrete distributions. This order retains desirable properties while relaxing structural constraints, thereby broadening applicability. We further introduce a class of variability measures based on probability concentration, offering robust and interpretable alternatives that conform to classical axioms. Empirical illustrations highlight the practical relevance of this framework. |
| title | An easily verifiable dispersion order for discrete distributions |
| topic | Methodology Statistics Theory |
| url | https://arxiv.org/abs/2506.23677 |