Cauchy–Logistic Unit Distribution: Properties and Application in Modeling Data Extremes
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 significan...
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| Format: | Article |
| Language: | English |
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2025-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/13/2/255 |
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| author | Vladica S. Stojanović Tanja Jovanović Spasojević Radica Bojičić Brankica Pažun Zlatko Langović |
| author_facet | Vladica S. Stojanović Tanja Jovanović Spasojević Radica Bojičić Brankica Pažun Zlatko Langović |
| author_sort | Vladica S. Stojanović |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-a0bf104b99564dfca6d79adb6334e586 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-a0bf104b99564dfca6d79adb6334e5862025-01-24T13:39:54ZengMDPI AGMathematics2227-73902025-01-0113225510.3390/math13020255Cauchy–Logistic Unit Distribution: Properties and Application in Modeling Data ExtremesVladica S. Stojanović0Tanja Jovanović Spasojević1Radica Bojičić2Brankica Pažun3Zlatko Langović4Department of Informatics & Computer Sciences, University of Criminal Investigation and Police Studies, 11000 Belgrade, SerbiaDepartment of Mathematics, Faculty of Sciences & Mathematics, University of Priština in Kosovska Mitrovica, 38220 Kosovska Mutrovica, SerbiaDepartment of Mathematics & Informatics, Faculty of Economics, University of Kosovska Mitrovica, 38220 Kosovska Mitrovica, SerbiaDepartment of Informatics, Mathematics and Statistics, Faculty of Engineering Management, 11000 Belgrade, SerbiaDepartment of Business Economy, Faculty of Hotel Management and Tourism, University of Kragujevac, 36210 Vrnjačka Banja, SerbiaThis 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.https://www.mdpi.com/2227-7390/13/2/255unit distributionsCauchy distributiongeneralized logistic mapstochastic propertiesparameter estimationquantiles |
| spellingShingle | Vladica S. Stojanović Tanja Jovanović Spasojević Radica Bojičić Brankica Pažun Zlatko Langović Cauchy–Logistic Unit Distribution: Properties and Application in Modeling Data Extremes Mathematics unit distributions Cauchy distribution generalized logistic map stochastic properties parameter estimation quantiles |
| title | Cauchy–Logistic Unit Distribution: Properties and Application in Modeling Data Extremes |
| title_full | Cauchy–Logistic Unit Distribution: Properties and Application in Modeling Data Extremes |
| title_fullStr | Cauchy–Logistic Unit Distribution: Properties and Application in Modeling Data Extremes |
| title_full_unstemmed | Cauchy–Logistic Unit Distribution: Properties and Application in Modeling Data Extremes |
| title_short | Cauchy–Logistic Unit Distribution: Properties and Application in Modeling Data Extremes |
| title_sort | cauchy logistic unit distribution properties and application in modeling data extremes |
| topic | unit distributions Cauchy distribution generalized logistic map stochastic properties parameter estimation quantiles |
| url | https://www.mdpi.com/2227-7390/13/2/255 |
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