Published

2019-07-01

A New Extended Mixture Skew Normal Distribution, With Applications

Una nueva mixtura de la distribución normal sesgada, con aplicaciones

DOI:

https://doi.org/10.15446/rce.v42n2.70087

Keywords:

Mixture distributions, Kurtosis, Skewness, Skew normal\linebreak distribution (en)
Distribuciones de mezclas, Kurtosis, Oblicuidad, Distribución normal sesgada (es)

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Authors

  • Haroon M. Barakat Zagazig University - Faculty of Science - Department of Mathematics
  • Abdallh W. Aboutahoun Alexandria University
  • Naeema El-kadar Alexandria University

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.

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). Además, se presenta una aplicación con un conjunto de datos reales de índice de masa corporal.

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How to Cite

APA

Barakat, H. M., Aboutahoun, A. W. and El-kadar, N. (2019). A New Extended Mixture Skew Normal Distribution, With Applications. Revista Colombiana de Estadística, 42(2), 167–183. https://doi.org/10.15446/rce.v42n2.70087

ACM

[1]
Barakat, H.M., Aboutahoun, A.W. and El-kadar, N. 2019. A New Extended Mixture Skew Normal Distribution, With Applications. Revista Colombiana de Estadística. 42, 2 (Jul. 2019), 167–183. DOI:https://doi.org/10.15446/rce.v42n2.70087.

ACS

(1)
Barakat, H. M.; Aboutahoun, A. W.; El-kadar, N. A New Extended Mixture Skew Normal Distribution, With Applications. Rev. colomb. estad. 2019, 42, 167-183.

ABNT

BARAKAT, H. M.; ABOUTAHOUN, A. W.; EL-KADAR, N. A New Extended Mixture Skew Normal Distribution, With Applications. Revista Colombiana de Estadística, [S. l.], v. 42, n. 2, p. 167–183, 2019. DOI: 10.15446/rce.v42n2.70087. Disponível em: https://revistas.unal.edu.co/index.php/estad/article/view/70087. Acesso em: 28 mar. 2025.

Chicago

Barakat, Haroon M., Abdallh W. Aboutahoun, and Naeema El-kadar. 2019. “A New Extended Mixture Skew Normal Distribution, With Applications”. Revista Colombiana De Estadística 42 (2):167-83. https://doi.org/10.15446/rce.v42n2.70087.

Harvard

Barakat, H. M., Aboutahoun, A. W. and El-kadar, N. (2019) “A New Extended Mixture Skew Normal Distribution, With Applications”, Revista Colombiana de Estadística, 42(2), pp. 167–183. doi: 10.15446/rce.v42n2.70087.

IEEE

[1]
H. M. Barakat, A. W. Aboutahoun, and N. El-kadar, “A New Extended Mixture Skew Normal Distribution, With Applications”, Rev. colomb. estad., vol. 42, no. 2, pp. 167–183, Jul. 2019.

MLA

Barakat, H. M., A. W. Aboutahoun, and N. El-kadar. “A New Extended Mixture Skew Normal Distribution, With Applications”. Revista Colombiana de Estadística, vol. 42, no. 2, July 2019, pp. 167-83, doi:10.15446/rce.v42n2.70087.

Turabian

Barakat, Haroon M., Abdallh W. Aboutahoun, and Naeema El-kadar. “A New Extended Mixture Skew Normal Distribution, With Applications”. Revista Colombiana de Estadística 42, no. 2 (July 1, 2019): 167–183. Accessed March 28, 2025. https://revistas.unal.edu.co/index.php/estad/article/view/70087.

Vancouver

1.
Barakat HM, Aboutahoun AW, El-kadar N. A New Extended Mixture Skew Normal Distribution, With Applications. Rev. colomb. estad. [Internet]. 2019 Jul. 1 [cited 2025 Mar. 28];42(2):167-83. Available from: https://revistas.unal.edu.co/index.php/estad/article/view/70087

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CrossRef citations4

1. A.I. Krasilnikov. (2023). Classification of Models of Two-component Mixtures of Symmetrical Distributions with Zero Kurtosis Coefficient. Èlektronnoe modelirovanie, 45(5), p.20. https://doi.org/10.15407/emodel.45.05.020.

2. H. M. Barakat, M. H. Dwes. (2022). Asymptotic behavior of ordered random variables in mixture of two Gaussian sequences with random index. AIMS Mathematics, 7(10), p.19306. https://doi.org/10.3934/math.20221060.

3. A.I. Krasilnikov. (2024). Modeling of Two-component Mixtures of Shifted Distributions with Zero Cumulant Coefficients. Èlektronnoe modelirovanie, 46(4), p.19. https://doi.org/10.15407/emodel.46.04.019.

4. A.I. Krasilnikov. (2024). Analysis of the Excess Kurtosis of Two-Component Mixtures of Shifted Non-Gaussian Distributions. Èlektronnoe modelirovanie, 46(2), p.15. https://doi.org/10.15407/emodel.46.02.015.

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