Statistical Papers, ( ISI ), Volume (55), No (2), Year (2014-4) , Pages (409-429)

Title : ( A generalized skew two-piece skew-elliptical distribution )

Authors: Seyed Mahdi Salehi , Ahad Jamalizadeh , Mahdi Doostparast ,

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We present a new generalized family of skew two-piece skew-elliptical (GSTPSE) models and derive some its statistical properties. It is shown that the new family of distribution may be written as a mixture of generalized skew elliptical distributions. Also, a new representation theorem for a special case of GSTPSE-distribution is given. Next, we will focus on $t$ kernel density and prove that it is a scale mixture of the generalized skew two-piece skew normal distributions. An explicit expression for the central moments as well as a recurrence relations for its cumulative distribution function and density are obtained. Since, this special case is a uni-/bimodal distribution, a sufficient condition for each cases is given. A real data set on heights of Australian females athletes is analysed. Finally, some concluding remarks and open problems are discussed.


, Multivariate elliptical distribution; Generalized skew two, piece skew, elliptical distribution; Generalized skew two, piece skew, $t$ distribution; Maximum likelihood
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author = {Salehi, Seyed Mahdi and Ahad Jamalizadeh and Doostparast, Mahdi},
title = {A generalized skew two-piece skew-elliptical distribution},
journal = {Statistical Papers},
year = {2014},
volume = {55},
number = {2},
month = {April},
issn = {0932-5026},
pages = {409--429},
numpages = {20},
keywords = {Multivariate elliptical distribution; Generalized skew two-piece skew-elliptical distribution; Generalized skew two-piece skew-$t$ distribution; Maximum likelihood estimator.},


%0 Journal Article
%T A generalized skew two-piece skew-elliptical distribution
%A Salehi, Seyed Mahdi
%A Ahad Jamalizadeh
%A Doostparast, Mahdi
%J Statistical Papers
%@ 0932-5026
%D 2014