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Title: Properties and applications of a new family of skew distributions
Authors: Gómez Déniz, Emilio 
Arnold, Barry C.
Sarabia, José M.
Gómez, Héctor W.
UNESCO Clasification: 530204 Estadística económica
530202 Modelos econométricos
Keywords: Logistic Distribution
Normal Distribution
Skew Normal Distribution
Symmetric Distribution
Issue Date: 2021
Project: Aportaciones A la Toma de Decisiones Bayesianas Óptimas: Aplicaciones Al Coste-Efectividad Con Datos Clínicos y Al Análisis de Riestos Con Datos Acturiales. 
Journal: Mathematics 
Abstract: 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.
ISSN: 2227-7390
DOI: 10.3390/math9010087
Source: Mathematics[EISSN 2227-7390],v. 9 (1), 87, (Enero 2021)
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