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arXiv · 2311.12634

On $q$-Order Statistics

Malvina Vamvakari
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Abstract

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.

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Malvina Vamvakari. 2023-11-21. On $q$-Order Statistics. https://arxiv.org/abs/2311.12634

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