Statistical Papers

, Volume 55, Issue 2, pp 409–429

A generalized skew two-piece skew-elliptical distribution


  • Mahdi Salehi
    • Department of StatisticsFerdowsi University of Mashhad
  • Ahad Jamalizadeh
    • Shahid Bahonar University of Kerman
    • Department of StatisticsFerdowsi University of Mashhad
Regular Article

DOI: 10.1007/s00362-012-0485-7

Cite this article as:
Salehi, M., Jamalizadeh, A. & Doostparast, M. Stat Papers (2014) 55: 409. doi:10.1007/s00362-012-0485-7


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 distributionGeneralized skew two-piece skew-elliptical distributionGeneralized skew two-piece skew-t distributionMaximum likelihood estimator

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© Springer-Verlag Berlin Heidelberg 2012