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Teoriya Veroyatnostei i ee Primeneniya, 2025, Volume 70, Issue 1, Pages 73–87
DOI: https://doi.org/10.4213/tvp5698 (Mi tvp5698) 		 
This article is cited in 1 scientific paper (total in 1 paper)

The Cauchy $q$-distribution: properties and simulations

Y. Amria, I. Boutouriaa, I. Bouzidaba

a Laboratory of Probability and Statistics, Sfax University, Sfax, Tunisia
b Abu Dhabi University, Abu Dhabi, UAE
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DOI: https://doi.org/10.4213/tvp5698
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
Published: 27.01.2025
English version:
Theory of Probability and its Applications, 2025, Volume 70, Issue 1, Pages 60–72
DOI: https://doi.org/10.1137/S0040585X97T992239
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: Y. Amri, I. Boutouria, I. Bouzida, “The Cauchy $q$-distribution: properties and simulations”, Teor. Veroyatnost. i Primenen., 70:1 (2025), 73–87; Theory Probab. Appl., 70:1 (2025), 60–72
Citation in format AMSBIB
\Bibitem{AmrBouBou25}
\by Y.~Amri, I.~Boutouria, I.~Bouzida
\paper The Cauchy $q$-distribution: properties and simulations
\jour Teor. Veroyatnost. i Primenen.
\yr 2025
\vol 70
\issue 1
\pages 73--87
\mathnet{http://mi.mathnet.ru/tvp5698}
\crossref{https://doi.org/10.4213/tvp5698}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=4856748}
\transl
\jour Theory Probab. Appl.
\yr 2025
\vol 70
\issue 1
\pages 60--72
\crossref{https://doi.org/10.1137/S0040585X97T992239}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-105005607899}
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  • https://doi.org/10.4213/tvp5698
  • https://www.mathnet.ru/eng/tvp/v70/i1/p73
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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