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Open AccessArticle

Normal-G Class of Probability Distributions: Properties and Applications

1
Department of Statistics and Informatics, Rural Federal University of Pernambuco, Recife 52171900, Pernambuco, Brazil
2
Federal Institute of Education, Science and Technology of Pernambuco, Recife 50740545, Pernambuco, Brazil
3
Department of Statistics, Paraíba State University, Campina Grande 58429500, Paraíba, Brazil
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(11), 1407; https://doi.org/10.3390/sym11111407
Received: 28 September 2019 / Revised: 22 October 2019 / Accepted: 12 November 2019 / Published: 15 November 2019
In this paper, we propose a novel class of probability distributions called Normal-G. 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-G 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. View Full-Text
Keywords: probabilistic distribution class; normal distribution; identifiability; maximum likelihood; moments probabilistic distribution class; normal distribution; identifiability; maximum likelihood; moments
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Silveira, F.V.J.; Gomes-Silva, F.; Brito, C.C.R.; Cunha-Filho, M.; Gusmão, F.R.S.; Xavier-Júnior, S.F.A. Normal-G Class of Probability Distributions: Properties and Applications. Symmetry 2019, 11, 1407.

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