Properties and Applications of a New Family of Skew Distributions

Emilio Gómez-Déniz, Barry C. Arnold, José M. Sarabia and Héctor W. Gómez
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Emilio Gómez-Déniz: Department of Quantitative Methods in Economics and TiDES Institute, University of Las Palmas de Gran Canaria, 35017 Las Palmas de Gran Canarias, Spain
Barry C. Arnold: Statistics Department, University of California Riverside, Riverside, CA 92504, USA
José M. Sarabia: Department of Quantitative Methods, CUNEF University, 28040 Madrid, Spain
Héctor W. Gómez: Departamento de Matemática, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile

Mathematics, 2021, vol. 9, issue 1, 1-18

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.

Keywords: logistic distribution; normal distribution; skew normal distribution; symmetric distribution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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