Abstract

BARAKAT, H. M.; ABOUTAHOUN, A. W.  and  EL-KADAR, N. N.. A New Extended Mixture Skew Normal Distribution, With Applications. Rev.Colomb.Estad. [online]. 2019, vol.42, n.2, pp.167-183. ISSN 0120-1751.  https://doi.org/10.15446/rce.v42n2.70087.

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.

Keywords : Mixture distributions; Kurtosis; Skewness; Skew normal distribution.

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