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A generalized skew two-piece skew-elliptical distribution

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  • Mahdi Salehi
  • Ahad Jamalizadeh
  • Mahdi Doostparast

Abstract

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. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Mahdi Salehi & Ahad Jamalizadeh & Mahdi Doostparast, 2014. "A generalized skew two-piece skew-elliptical distribution," Statistical Papers, Springer, vol. 55(2), pages 409-429, May.
    • Handle: RePEc:spr:stpapr:v:55:y:2014:i:2:p:409-429
    DOI: 10.1007/s00362-012-0485-7
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    References listed on IDEAS

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    1. Jamalizadeh, A. & Mehrali, Y. & Balakrishnan, N., 2009. "Recurrence relations for bivariate t and extended skew-t distributions and an application to order statistics from bivariate t," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4018-4027, October.
    2. Jamalizadeh, A. & Balakrishnan, N., 2010. "Distributions of order statistics and linear combinations of order statistics from an elliptical distribution as mixtures of unified skew-elliptical distributions," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1412-1427, July.
    3. Jamalizadeh, A. & Khosravi, M. & Balakrishnan, N., 2009. "Recurrence relations for distributions of a skew-t and a linear combination of order statistics from a bivariate-t," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 847-852, February.
    4. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389, May.
    5. Álvarez Alvarado, Marcos Tulio, 2003. "¿Existe una alternativa al capitalismo?," Observatorio de la Economía Latinoamericana, Servicios Académicos Intercontinentales SL. Hasta 31/12/2022, issue 16, November.
    6. Cambanis, Stamatis & Huang, Steel & Simons, Gordon, 1981. "On the theory of elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 368-385, September.
    7. Jamalizadeh, A. & Balakrishnan, N. & Salehi, Mehdi, 2010. "Order statistics and linear combination of order statistics arising from a bivariate selection normal distribution," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 445-451, March.
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    1. Mahdi Salehi & Mahdi Doostparast, 2015. "Expressions for moments of order statistics and records from the skew-normal distribution in terms of multivariate normal orthant probabilities," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(4), pages 547-568, November.

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