A Symmetric/Asymmetric Bimodal Extension Based on the Logistic Distribution: Properties, Simulation and Applications
In this paper, we introduce bimodal extensions, one symmetric and one asymmetric, of the logistic distribution. We define this new density and study some basic properties. We draw inferences from the moment estimator and maximum likelihood approaches. We present a simulation study to assess the beha...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/12/1968 |
| _version_ | 1797484741684887552 |
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| author | Isaac E. Cortés Osvaldo Venegas Héctor W. Gómez |
| author_facet | Isaac E. Cortés Osvaldo Venegas Héctor W. Gómez |
| author_sort | Isaac E. Cortés |
| collection | DOAJ |
| description | In this paper, we introduce bimodal extensions, one symmetric and one asymmetric, of the logistic distribution. We define this new density and study some basic properties. We draw inferences from the moment estimator and maximum likelihood approaches. We present a simulation study to assess the behaviour of the moment and maximum likelihood estimators. We also study the singularity of the Fisher information matrix for particular cases. We offer applications in real data and compare them with a mixture of logistics distributions. |
| first_indexed | 2024-03-09T23:09:45Z |
| format | Article |
| id | doaj.art-666823fc4a044396b638a1d08a893a78 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T23:09:45Z |
| publishDate | 2022-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-666823fc4a044396b638a1d08a893a782023-11-23T17:47:30ZengMDPI AGMathematics2227-73902022-06-011012196810.3390/math10121968A Symmetric/Asymmetric Bimodal Extension Based on the Logistic Distribution: Properties, Simulation and ApplicationsIsaac E. Cortés0Osvaldo Venegas1Héctor W. Gómez2Inter-Institutional Graduation Program in Statistics, Universidade de São Paulo, São Paulo 05508-090, BrazilDepartamento de Ciencias Matemáticas y Físicas, Facultad de Ingeniería, Universidad Católica de Temuco, Temuco 4780000, ChileDepartamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, ChileIn this paper, we introduce bimodal extensions, one symmetric and one asymmetric, of the logistic distribution. We define this new density and study some basic properties. We draw inferences from the moment estimator and maximum likelihood approaches. We present a simulation study to assess the behaviour of the moment and maximum likelihood estimators. We also study the singularity of the Fisher information matrix for particular cases. We offer applications in real data and compare them with a mixture of logistics distributions.https://www.mdpi.com/2227-7390/10/12/1968bimodal distributionlogistic distributionmaximum likelihoodsymmetryasymmetric |
| spellingShingle | Isaac E. Cortés Osvaldo Venegas Héctor W. Gómez A Symmetric/Asymmetric Bimodal Extension Based on the Logistic Distribution: Properties, Simulation and Applications Mathematics bimodal distribution logistic distribution maximum likelihood symmetry asymmetric |
| title | A Symmetric/Asymmetric Bimodal Extension Based on the Logistic Distribution: Properties, Simulation and Applications |
| title_full | A Symmetric/Asymmetric Bimodal Extension Based on the Logistic Distribution: Properties, Simulation and Applications |
| title_fullStr | A Symmetric/Asymmetric Bimodal Extension Based on the Logistic Distribution: Properties, Simulation and Applications |
| title_full_unstemmed | A Symmetric/Asymmetric Bimodal Extension Based on the Logistic Distribution: Properties, Simulation and Applications |
| title_short | A Symmetric/Asymmetric Bimodal Extension Based on the Logistic Distribution: Properties, Simulation and Applications |
| title_sort | symmetric asymmetric bimodal extension based on the logistic distribution properties simulation and applications |
| topic | bimodal distribution logistic distribution maximum likelihood symmetry asymmetric |
| url | https://www.mdpi.com/2227-7390/10/12/1968 |
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