A Generalized Rayleigh Family of Distributions Based on the Modified Slash Model
Specifying a proper statistical model to represent asymmetric lifetime data with high kurtosis is an open problem. In this paper, the three-parameter, modified, slashed, generalized Rayleigh family of distributions is proposed. Its structural properties are studied: stochastic representation, probab...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-07-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/7/1226 |
| _version_ | 1797525974359736320 |
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| author | Inmaculada Barranco-Chamorro Yuri A. Iriarte Yolanda M. Gómez Juan M. Astorga Héctor W. Gómez |
| author_facet | Inmaculada Barranco-Chamorro Yuri A. Iriarte Yolanda M. Gómez Juan M. Astorga Héctor W. Gómez |
| author_sort | Inmaculada Barranco-Chamorro |
| collection | DOAJ |
| description | Specifying a proper statistical model to represent asymmetric lifetime data with high kurtosis is an open problem. In this paper, the three-parameter, modified, slashed, generalized Rayleigh family of distributions is proposed. Its structural properties are studied: stochastic representation, probability density function, hazard rate function, moments and estimation of parameters via maximum likelihood methods. As merits of our proposal, we highlight as particular cases a plethora of lifetime models, such as Rayleigh, Maxwell, half-normal and chi-square, among others, which are able to accommodate heavy tails. A simulation study and applications to real data sets are included to illustrate the use of our results. |
| first_indexed | 2024-03-10T09:21:39Z |
| format | Article |
| id | doaj.art-419b4f3fb8ef48548ebb3b6033ab3493 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T09:21:39Z |
| publishDate | 2021-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-419b4f3fb8ef48548ebb3b6033ab34932023-11-22T05:09:09ZengMDPI AGSymmetry2073-89942021-07-01137122610.3390/sym13071226A Generalized Rayleigh Family of Distributions Based on the Modified Slash ModelInmaculada Barranco-Chamorro0Yuri A. Iriarte1Yolanda M. Gómez2Juan M. Astorga3Héctor W. Gómez4Departamento de Estadística e Investigación Operativa, Facultad de Matemáticas, Universidad de Sevilla, 41012 Sevilla, SpainDepartamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, ChileDepartamento de Matemáticas, Facultad de Ingeniería, Universidad de Atacama, Copiapó 1530000, ChileDepartamento de Tecnologías de la Energía, Facultad Tecnológica, Universidad de Atacama, Copiapó 1530000, ChileDepartamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, ChileSpecifying a proper statistical model to represent asymmetric lifetime data with high kurtosis is an open problem. In this paper, the three-parameter, modified, slashed, generalized Rayleigh family of distributions is proposed. Its structural properties are studied: stochastic representation, probability density function, hazard rate function, moments and estimation of parameters via maximum likelihood methods. As merits of our proposal, we highlight as particular cases a plethora of lifetime models, such as Rayleigh, Maxwell, half-normal and chi-square, among others, which are able to accommodate heavy tails. A simulation study and applications to real data sets are included to illustrate the use of our results.https://www.mdpi.com/2073-8994/13/7/1226generalized Rayleigh distributionEM algorithmkurtosismaximum likelihood estimationslashed generalized Rayleigh distribution |
| spellingShingle | Inmaculada Barranco-Chamorro Yuri A. Iriarte Yolanda M. Gómez Juan M. Astorga Héctor W. Gómez A Generalized Rayleigh Family of Distributions Based on the Modified Slash Model Symmetry generalized Rayleigh distribution EM algorithm kurtosis maximum likelihood estimation slashed generalized Rayleigh distribution |
| title | A Generalized Rayleigh Family of Distributions Based on the Modified Slash Model |
| title_full | A Generalized Rayleigh Family of Distributions Based on the Modified Slash Model |
| title_fullStr | A Generalized Rayleigh Family of Distributions Based on the Modified Slash Model |
| title_full_unstemmed | A Generalized Rayleigh Family of Distributions Based on the Modified Slash Model |
| title_short | A Generalized Rayleigh Family of Distributions Based on the Modified Slash Model |
| title_sort | generalized rayleigh family of distributions based on the modified slash model |
| topic | generalized Rayleigh distribution EM algorithm kurtosis maximum likelihood estimation slashed generalized Rayleigh distribution |
| url | https://www.mdpi.com/2073-8994/13/7/1226 |
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