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Properties and applications of a new family of skew distributions

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.

Otras publicaciones de la misma revista o congreso con autores/as de la Universidad de Cantabria

 Fuente: Mathematics , Vol. 9, Issue 1, Pages 1 - 18, Article number 87

Editorial: MDPI

 Fecha de publicación: 01/01/2021

Nº de páginas: 18

Tipo de publicación: Artículo de Revista

 DOI: 10.3390/math9010087

ISSN: 2227-7390

Autoría

GÓMEZ-DÉNIZ, E.

ARNOLD, BARRY C.

GÓMEZ, HÉCTOR W.