Properties and Applications of a New Family of Skew Distributions
We introduce two families of continuous distribution functions with not-necessarily symmetric densities, which contain a parent distribution as a special case. The two families proposed depend on two parameters and are presented as an alternative to the skew normal distribution and other proposals i...
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| Format: | Article |
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MDPI AG
2021-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/1/87 |
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| author | Emilio Gómez-Déniz Barry C. Arnold José M. Sarabia Héctor W. Gómez |
| author_facet | Emilio Gómez-Déniz Barry C. Arnold José M. Sarabia Héctor W. Gómez |
| author_sort | Emilio Gómez-Déniz |
| collection | DOAJ |
| description | We introduce two families of continuous distribution functions with not-necessarily symmetric densities, which contain a parent distribution as a special case. The two families proposed depend on two parameters and are presented as an alternative to the skew normal distribution and other proposals in the statistical literature. The density functions of these new families are given by a closed expression which allows us to easily compute probabilities, moments and related quantities. The second family can exhibit bimodality and its standardized fourth central moment (kurtosis) can be lower than that of the Azzalini skew normal distribution. Since the second proposed family can be bimodal we fit two well-known data set with this feature as applications. We concentrate attention on the case in which the normal distribution is the parent distribution but some consideration is given to other parent distributions, such as the logistic distribution. |
| first_indexed | 2024-03-10T13:32:10Z |
| format | Article |
| id | doaj.art-ae2bd67a694049e6b9b0fc6419af8c63 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T13:32:10Z |
| publishDate | 2021-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-ae2bd67a694049e6b9b0fc6419af8c632023-11-21T07:54:43ZengMDPI AGMathematics2227-73902021-01-01918710.3390/math9010087Properties and Applications of a New Family of Skew DistributionsEmilio Gómez-Déniz0Barry C. Arnold1José M. Sarabia2Héctor W. Gómez3Department of Quantitative Methods in Economics and TiDES Institute, University of Las Palmas de Gran Canaria, 35017 Las Palmas de Gran Canarias, SpainStatistics Department, University of California Riverside, Riverside, CA 92504, USADepartment of Quantitative Methods, CUNEF University, 28040 Madrid, SpainDepartamento de Matemática, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, ChileWe introduce two families of continuous distribution functions with not-necessarily symmetric densities, which contain a parent distribution as a special case. The two families proposed depend on two parameters and are presented as an alternative to the skew normal distribution and other proposals in the statistical literature. The density functions of these new families are given by a closed expression which allows us to easily compute probabilities, moments and related quantities. The second family can exhibit bimodality and its standardized fourth central moment (kurtosis) can be lower than that of the Azzalini skew normal distribution. Since the second proposed family can be bimodal we fit two well-known data set with this feature as applications. We concentrate attention on the case in which the normal distribution is the parent distribution but some consideration is given to other parent distributions, such as the logistic distribution.https://www.mdpi.com/2227-7390/9/1/87logistic distributionnormal distributionskew normal distributionsymmetric distribution |
| spellingShingle | Emilio Gómez-Déniz Barry C. Arnold José M. Sarabia Héctor W. Gómez Properties and Applications of a New Family of Skew Distributions Mathematics logistic distribution normal distribution skew normal distribution symmetric distribution |
| title | Properties and Applications of a New Family of Skew Distributions |
| title_full | Properties and Applications of a New Family of Skew Distributions |
| title_fullStr | Properties and Applications of a New Family of Skew Distributions |
| title_full_unstemmed | Properties and Applications of a New Family of Skew Distributions |
| title_short | Properties and Applications of a New Family of Skew Distributions |
| title_sort | properties and applications of a new family of skew distributions |
| topic | logistic distribution normal distribution skew normal distribution symmetric distribution |
| url | https://www.mdpi.com/2227-7390/9/1/87 |
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