A New Extended Mixture Skew Normal Distribution, With Applications

• Autores: H.M. Barakat, A. W. Aboutahoun, N. N. El-kadar
• Localización: Revista Colombiana de Estadística, ISSN-e 2389-8976, ISSN 0120-1751, Vol. 42, Nº. 2, 2019, págs. 167-183
• Idioma: inglés
• DOI: 10.15446/rce.v42n2.70087
• Títulos paralelos:
  • Una nueva mixtura de la distribución normal sesgada, con aplicaciones
• Enlaces
  • Texto completo
• Resumen
  • español

    Resumen 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.

  • English

    Abstract 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.

• Referencias bibliográficas
  • Akaike, H.,Petrov, B. N.,Csaki, F. (1973). Information theory and the maximum likelihood principle, in. SecondInternational Symposium on...
  • Al-Hussaini, E. K.,Ahsanullah, M. (2015). Exponentiated distributions. Atlantis Press. Paris, France.
  • Alzaatreh, A. (2011). A new method for generating families of continuous distributions. Central Michigan University Mount Pleasant. Michigan....
  • Alzaatreh, A.,Famoye, F.,Lee, C. (2013). ‘A new method for generating families of continuous distributions’. Metron. 71. 63-79
  • Arellano-Valle, R. B.,Gomez, H. W.,Quintana, F. A. (2004). ‘A new class of skew-normal distribution’. Communications in Statistics-Theory...
  • Azzalini, A. (1985). ‘A class of distributions which includes the normal ones’. Scandinavian Journal of Statistics. 12. 171
  • Azzalini, A.,Capitanio, A. (2014). The skew-normal and related families. Cambridge University Press. New York.
  • Barakat, H. M. (2015). ‘A new method for adding two parameters to a family of distributions with application to the normal and exponential...
  • Barakat, H. M.,Aboutahoun, A. W.,El-kadar, N. N. (2019). ‘On some generalized families arising from mixture normal distribution with applications’....
  • Barakat, H. M.,Ghitany, M. E.,Al-Hussaini, E. K. (2009). ‘Asymptotic distributions of order statistics and record values under the Marshall-Olkin...
  • Barakat, H. M.,Khaled, O. M. (2017). ‘Towards the establishment of a family of distributions that best fits any data set’. Communication in...
  • Barakat, H. M.,Nigm, E. M. (2014). ‘Asymptotic distributions of order statistics and record values arising from the class of beta-generated...
  • Barakat, H. M.,Nigm, E. M.,Harpy, M. H. (2017). ‘Limit theorems of order statistics and record values from the gamma and Kumaraswamy-generated-distributions’....
  • Barreto-Souza, W.,Lemonte, A.,Cordeiro, G. M. (2013). ‘General results for Marshall and Olkin’s family of distributions’. Anais da Academia...
  • Box, G. E. P.,Tiao, G. C. (1973). Bayesian Inference in Statistical Analysis. Addision-Wesley, Reading. MA.
  • Cordeiro, G. M.,Castro, M. (2011). ‘A new family of generalized distributions’. Journal of Statistical Computation and Simulation. 81. 883
  • Cordeiro, G. M.,Lemonte, A. J.,Ortiga, E. E. M. (2014). ‘The Marshall-Olkin family of distributions: Mathematical properties and new models’....
  • Cordeiro, G. M.,Ortiga, E. E. M.,Silva, G. O. (2014). ‘The Kumaraswamy modified Weibull distribution: Theory and applications’. Journal of...
  • Correa, M. A.,Nogueira, D. A.,Ferreira, E. B. (2012). ‘Kumaraswamy normal and Azzalini’s skew normal modeling asymmetry’. Sigmae. 1. 65-83
  • Doğru, F. Z.,Arslan, O. (2017). ‘Robust mixture regression based on the skew t distribution’. Revista Colombiana de Estadistica. 40. 45-64
  • Ellison, A. M. (1987). ‘Effect of seed dimorphism on the density-dependent dynamics of experimental populations of Atriplex triangularis (Chenopodiaceae)’....
  • Eugene, N.,Lee, C.,Famoye, F. (2002). ‘Beta-normal distribution and its application’. Communications in Statistics-Theory and Methods. 31....
  • Ho, N. (2017). Parameter estimation and multilevel clustering with mixture and hierarchical models. University of Michigan. Michigan.
  • Ho, N.,Nguyen, X. (2016). Singularity structures and impacts on parameter estimation in finite mixtures of distributions. Cornell University....
  • Jones, M. C. (2004). ‘Families of distributions arising from distributions of order statistics’. Test. 13. 1-43
  • Jose, K. K. (2011). Marshall-olkin family of distributions and their applications in reliability theory, time series modeling and stress strength...
  • Lemonte, A. J. (2014). ‘The beta log-logistic distribution’. Brazilian Journal of Probability and Statistics. 28. 313
  • Mameli, V.,Musio, M. (2013). ‘Generalization of the Skew-Normal Distribution: The Beta skew-normal’. Communications in Statistics-Theory and...
  • Marshall, A. W.,Olkin, I. (1997). ‘A new method for adding a prameter to a family of distributions with application to the exponential and...
  • Martinez-Florez, G.,Vergara-Cardozo, S.,Gonzalez, L. M. (2013). ‘The family of log-skew-normal alpha-power distributions using precipitation...
  • McLachlan, G.,Peel, D. (2000). Finite mixture models, Wiley Series in Probability and Statististics.
  • Nadarajah, S. (2005). ‘A generalized normal distribution’. Journal of Applied Statistics. 32. 685
  • Perez-Rodriguez, P.,Villasenor, J. A.,Perezc, S.,Suarez, J. (2017). ‘Bayesian estimation for the centered parameterization of the skew-normal...
  • Popović, B. V.,Cordeiro, G. M.,Pascoa, M. A. R. (2017). ‘A new extended mixture normal distribution’. Mathematical Communications. 22. 53-73
  • Schwarz, G. (1978). ‘Estimating the dimension of a model’. Annals of Statistics. 6. 461
  • Titterington, D. M.,Smith, A. F. M.,Makov, U. E. (1986). Statistical analysis of finite mixture distributions. Wiley. New York.