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

Vladica S. Stojanović (), Tanja Jovanović Spasojević, Radica Bojičić, Brankica Pažun and Zlatko Langović
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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

Mathematics, 2025, vol. 13, issue 2, 1-23

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.

Keywords: unit distributions; Cauchy distribution; generalized logistic map; stochastic properties; parameter estimation; quantiles; application (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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