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Cauchy–Logistic Unit Distribution: Properties and Application in Modeling Data Extremes

Author

Listed:
  • Vladica S. Stojanović

    (Department of Informatics & Computer Sciences, University of Criminal Investigation and Police Studies, 11000 Belgrade, Serbia)

  • Tanja Jovanović Spasojević

    (Department of Mathematics, Faculty of Sciences & Mathematics, University of Priština in Kosovska Mitrovica, 38220 Kosovska Mutrovica, Serbia)

  • Radica Bojičić

    (Department of Mathematics & Informatics, Faculty of Economics, University of Kosovska Mitrovica, 38220 Kosovska Mitrovica, Serbia)

  • Brankica Pažun

    (Department of Informatics, Mathematics and Statistics, Faculty of Engineering Management, 11000 Belgrade, Serbia)

  • Zlatko Langović

    (Department of Business Economy, Faculty of Hotel Management and Tourism, University of Kragujevac, 36210 Vrnjačka Banja, Serbia)

Abstract

This manuscript deals with a novel two-parameter stochastic distribution, obtained by transforming the Cauchy distribution, using generalized logistic mapping, into a unit interval. In this way, according to the well-known properties of the Cauchy distribution, a unit random variable with significantly accentuated values at the ends of the unit interval is obtained. Therefore, the proposed stochastic distribution, named the Cauchy–logistic unit distribution, represents a stochastic model that may be suitable for modeling phenomena and processes with emphasized extreme values. Key stochastic properties of the CLU distribution are examined, such as moments, entropy, modality, and symmetry conditions. In addition, a quantile-based parameter estimation procedure, an asymptotic analysis of the thus obtained estimators, and their Monte Carlo simulation study are conducted. Finally, the application of the proposed distribution in stochastic modeling of some real-world data with emphasized extreme values is provided.

Suggested Citation

  • Vladica S. Stojanović & Tanja Jovanović Spasojević & Radica Bojičić & Brankica Pažun & Zlatko Langović, 2025. "Cauchy–Logistic Unit Distribution: Properties and Application in Modeling Data Extremes," Mathematics, MDPI, vol. 13(2), pages 1-23, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:2:p:255-:d:1566659
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    References listed on IDEAS

    as
    1. Dagmara Dudek & Anna Kuczmaszewska, 2024. "Some practical and theoretical issues related to the quantile estimators," Statistical Papers, Springer, vol. 65(6), pages 3917-3933, August.
    2. Vladica S. Stojanović & Tanja Jovanović Spasojević & Mihailo Jovanović, 2024. "Laplace-Logistic Unit Distribution with Application in Dynamic and Regression Analysis," Mathematics, MDPI, vol. 12(14), pages 1-21, July.
    3. McDonald, James B. & Xu, Yexiao J., 1995. "A generalization of the beta distribution with applications," Journal of Econometrics, Elsevier, vol. 69(2), pages 427-428, October.
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