The Cauchy $q$-Distribution: Properties and Simulations

In this paper, we present a $q$-calculus-based generalization of the Cauchy distribution. We explore a range of characteristics associated with this distribution, encompassing $q$-moments, $q$-variance, and $q$-cumulative functions. Additionally, we formulate parameter estimation techniques employing the fixed point method. To evaluate the efficacy of these $q$-distributions, we carry out simulation studies, offering valuable insights into their performance.