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 distribution Generalized skew two-piece skew-elliptical distribution Generalized skew two-piece skew-t distribution Maximum likelihood estimator