Statistical Papers

, Volume 55, Issue 2, pp 409–429 | Cite as

A generalized skew two-piece skew-elliptical distribution

  • Mahdi Salehi
  • Ahad Jamalizadeh
  • Mahdi Doostparast
Regular Article


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 estimator 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Mahdi Salehi
    • 1
  • Ahad Jamalizadeh
    • 2
  • Mahdi Doostparast
    • 1
  1. 1.Department of StatisticsFerdowsi University of MashhadMashhadIran
  2. 2.Shahid Bahonar University of KermanKermanIran

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