This article is cited in 1 paper

The Cauchy $q$-distribution: properties and simulations

Y. Amri^a, I. Boutouria^a, I. Bouzida<sup>ba

a</sup> Laboratory of Probability and Statistics, Sfax University, Sfax, Tunisia
^b Abu Dhabi University, Abu Dhabi, UAE

Abstract: 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.

Keywords: $q$-calculus, $q$-Cauchy distribution, $q$-uniform distribution.

Received: 07.01.2024
Revised: 21.11.2024
Accepted: 05.02.2024

DOI: 10.4213/tvp5698

 English version: Theory of Probability and its Applications, 2025, 70:1, 60–72

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