Normal-<i>G</i> Class of Probability Distributions: Properties and Applications
In this paper, we propose a novel class of probability distributions called Normal-<i>G</i>. It has the advantage of demanding no additional parameters besides those of the parent distribution, thereby providing parsimonious models. Furthermore, the class enjoys the property of identifia...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-11-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/11/11/1407 |
| _version_ | 1817988050746081280 |
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| author | Fábio V. J. Silveira Frank Gomes-Silva Cícero C. R. Brito Moacyr Cunha-Filho Felipe R. S. Gusmão Sílvio F. A. Xavier-Júnior |
| author_facet | Fábio V. J. Silveira Frank Gomes-Silva Cícero C. R. Brito Moacyr Cunha-Filho Felipe R. S. Gusmão Sílvio F. A. Xavier-Júnior |
| author_sort | Fábio V. J. Silveira |
| collection | DOAJ |
| description | In this paper, we propose a novel class of probability distributions called Normal-<i>G</i>. It has the advantage of demanding no additional parameters besides those of the parent distribution, thereby providing parsimonious models. Furthermore, the class enjoys the property of identifiability whenever the baseline is identifiable. We present special Normal-<i>G</i> sub-models, which can fit asymmetrical data with either positive or negative skew. Other important mathematical properties are described, such as the series expansion of the probability density function (pdf), which is used to derive expressions for the moments and the moment generating function (mgf). We bring Monte Carlo simulation studies to investigate the behavior of the maximum likelihood estimates (MLEs) of two distributions generated by the class and we also present applications to real datasets to illustrate its usefulness. |
| first_indexed | 2024-04-14T00:29:25Z |
| format | Article |
| id | doaj.art-a43f1a7754c44dd5a8fcf8fe89baa7e4 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-14T00:29:25Z |
| publishDate | 2019-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-a43f1a7754c44dd5a8fcf8fe89baa7e42022-12-22T02:22:35ZengMDPI AGSymmetry2073-89942019-11-011111140710.3390/sym11111407sym11111407Normal-<i>G</i> Class of Probability Distributions: Properties and ApplicationsFábio V. J. Silveira0Frank Gomes-Silva1Cícero C. R. Brito2Moacyr Cunha-Filho3Felipe R. S. Gusmão4Sílvio F. A. Xavier-Júnior5Department of Statistics and Informatics, Rural Federal University of Pernambuco, Recife 52171900, Pernambuco, BrazilDepartment of Statistics and Informatics, Rural Federal University of Pernambuco, Recife 52171900, Pernambuco, BrazilFederal Institute of Education, Science and Technology of Pernambuco, Recife 50740545, Pernambuco, BrazilDepartment of Statistics and Informatics, Rural Federal University of Pernambuco, Recife 52171900, Pernambuco, BrazilDepartment of Statistics and Informatics, Rural Federal University of Pernambuco, Recife 52171900, Pernambuco, BrazilDepartment of Statistics, Paraíba State University, Campina Grande 58429500, Paraíba, BrazilIn this paper, we propose a novel class of probability distributions called Normal-<i>G</i>. It has the advantage of demanding no additional parameters besides those of the parent distribution, thereby providing parsimonious models. Furthermore, the class enjoys the property of identifiability whenever the baseline is identifiable. We present special Normal-<i>G</i> sub-models, which can fit asymmetrical data with either positive or negative skew. Other important mathematical properties are described, such as the series expansion of the probability density function (pdf), which is used to derive expressions for the moments and the moment generating function (mgf). We bring Monte Carlo simulation studies to investigate the behavior of the maximum likelihood estimates (MLEs) of two distributions generated by the class and we also present applications to real datasets to illustrate its usefulness.https://www.mdpi.com/2073-8994/11/11/1407probabilistic distribution classnormal distributionidentifiabilitymaximum likelihoodmoments |
| spellingShingle | Fábio V. J. Silveira Frank Gomes-Silva Cícero C. R. Brito Moacyr Cunha-Filho Felipe R. S. Gusmão Sílvio F. A. Xavier-Júnior Normal-<i>G</i> Class of Probability Distributions: Properties and Applications Symmetry probabilistic distribution class normal distribution identifiability maximum likelihood moments |
| title | Normal-<i>G</i> Class of Probability Distributions: Properties and Applications |
| title_full | Normal-<i>G</i> Class of Probability Distributions: Properties and Applications |
| title_fullStr | Normal-<i>G</i> Class of Probability Distributions: Properties and Applications |
| title_full_unstemmed | Normal-<i>G</i> Class of Probability Distributions: Properties and Applications |
| title_short | Normal-<i>G</i> Class of Probability Distributions: Properties and Applications |
| title_sort | normal i g i class of probability distributions properties and applications |
| topic | probabilistic distribution class normal distribution identifiability maximum likelihood moments |
| url | https://www.mdpi.com/2073-8994/11/11/1407 |
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