  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.
