Regular Article

Statistical Papers

, Volume 55, Issue 2, pp 409-429

First online:

A generalized skew two-piece skew-elliptical distribution

  • Mahdi SalehiAffiliated withDepartment of Statistics, Ferdowsi University of Mashhad
  • , Ahad JamalizadehAffiliated withShahid Bahonar University of Kerman
  • , Mahdi DoostparastAffiliated withDepartment of Statistics, Ferdowsi University of Mashhad Email author 

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


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