On $q$-Order Statistics
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866917363704659968 |
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| author | Vamvakari, Malvina |
| author_facet | Vamvakari, Malvina |
| contents | Building on the notion of $q$-integral introduced by Thomae in 1869, we introduce $q$-order statistics (that, is $q$-analogues of the classical order statistics, for $0<q<1$) which arise from dependent and not identically distributed $q$-continuous random variables and study their distributional properties. We study the $q$-distribution functions and the $q$-density functions of the relative $q$-ordered random variables. We focus on $q$-ordered variables arising from dependent and not identically $q$-uniformly distributed random variables and we derive their $q$-distributions, including $q$-power law, $q$-beta and $q$-Dirichlet distributions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_12634 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On $q$-Order Statistics Vamvakari, Malvina Probability Statistics Theory 62E15, 62B05, 60C05, 60E05, 62b05, 62G30, 05A30 Building on the notion of $q$-integral introduced by Thomae in 1869, we introduce $q$-order statistics (that, is $q$-analogues of the classical order statistics, for $0<q<1$) which arise from dependent and not identically distributed $q$-continuous random variables and study their distributional properties. We study the $q$-distribution functions and the $q$-density functions of the relative $q$-ordered random variables. We focus on $q$-ordered variables arising from dependent and not identically $q$-uniformly distributed random variables and we derive their $q$-distributions, including $q$-power law, $q$-beta and $q$-Dirichlet distributions. |
| title | On $q$-Order Statistics |
| topic | Probability Statistics Theory 62E15, 62B05, 60C05, 60E05, 62b05, 62G30, 05A30 |
| url | https://arxiv.org/abs/2311.12634 |