Malvina Vamvakari
Published 2023-11-21Version 1
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.
Rounding of continuous random variables and oscillatory asymptotics
A simple proof of the theorem of Sklar and its extension to distribution functions
A New Type Of Upper And Lower Bounds On Right-Tail Probabilities Of Continuous Random Variables
![QR code for arXiv:2311.12634 [math.PR]](http://oss.arxitics.com/images/favicon.svg)