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Revista Colombiana de Estadística

Print version ISSN 0120-1751

Rev.Colomb.Estad. vol.42 no.2 Bogotá July/Dec. 2019 

Artículos originales de investigación

A New Extended Mixture Skew Normal Distribution, With Applications

Una nueva mixtura de la distribución normal sesgada, con aplicaciones

H. M. Barakata  , A. W. Aboutahounb  , N. N. El-kadarc 

aDepartment of Mathematics, Faculty of Science, Universidad de Zagazig, Zagazig, Egypt. E-mail:

bDepartment of Statistics institution, Alexandria, Egypt. E-mail:

cDepartment of Statistics institution, Alexandria, Egypt. E-mail:


One of the most important property of the mixture normal distributions model is its flexibility to accommodate various types of distribution functions (df’s). We show that the mixture of the skew normal distribution and its reverse, after adding a location parameter to the skew normal distribution, and adding the same location parameter with different sign to its reverse is a family of df’s that contains all the possible types of df’s. Besides, it has a very remarkable wide range of the indices of skewness and kurtosis. Computational techniques using EM-type algorithms are employed for iteratively computing maximum likelihood estimates of the model parameters. Moreover, an application with a body mass index real data set is presented.

Key words: Mixture distributions; Kurtosis; Skewness; Skew normal distribution


Una de las propiedades más importantes de la mezcla del modelo de distribuciones normales es su flexibilidad para acomodar varios tipos de funciones de distribución (fd). Mostramos que la mixtura de la distribución normal sesgada y su inversa, después de agregar un parámetro de ubicación a la distribución normal sesgada, y agregar el mismo parámetro de ubicación con un signo diferente a su inversa, es una familia de fd que contiene todos los tipos posibles de fd. Además, posee una muy amplia gama de índices de asimetría y curtosis. Las técnicas computacionales que se utilizan para calcular de forma iterativa las estimaciones de máxima verosimilitud de los parámetros del modelo es el algoritmo de esperanza-maximización (EM). mas, se presenta una aplicación con un conjunto de datos reales de índice de masa corporal.

Palabras-clave: Distribuciones de mezclas; Curtosis; Oblicuidad; Distribución normal sesgada

Full text available only in PDF format.


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