A generalized skew two-piece skew-elliptical distribution

作者：Salehi Mahdi; Jamalizadeh Ahad; Doostparast Mahdi^*

来源：Statistical Papers, 2014, 55(2): 409-429.

DOI：10.1007/s00362-012-0485-7

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

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.

• 出版日期2014-5