The Bunching and Monotonicity Properties of Families of Probability Distributions
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910472778809344 |
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| author | Portnoy, S. Torrado, N. Veerman, J. J. P. |
| author_facet | Portnoy, S. Torrado, N. Veerman, J. J. P. |
| contents | Measuring the concentration of random variables is a fundamental concept in probability and statistics. Here, we explore a type of concentration measure for continuous random variables with bounded support and use it to provide a notion of stochastic order by concentration. We give an application to the Beta family of distributions, and specifically to the one-parameter subfamily with constant mean. This leads to using U.S. household income data to fit generalized Beta distributions and offers a new measure of income concentration. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_02894 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Bunching and Monotonicity Properties of Families of Probability Distributions Portnoy, S. Torrado, N. Veerman, J. J. P. Statistics Theory 60E15, 62E99 Measuring the concentration of random variables is a fundamental concept in probability and statistics. Here, we explore a type of concentration measure for continuous random variables with bounded support and use it to provide a notion of stochastic order by concentration. We give an application to the Beta family of distributions, and specifically to the one-parameter subfamily with constant mean. This leads to using U.S. household income data to fit generalized Beta distributions and offers a new measure of income concentration. |
| title | The Bunching and Monotonicity Properties of Families of Probability Distributions |
| topic | Statistics Theory 60E15, 62E99 |
| url | https://arxiv.org/abs/2406.02894 |