Noncentral quadratic forms of the skew elliptical variables
AbstractIn this paper the quadratic forms in the skew elliptical variables are studied. A family of the noncentral generalized Dirichlet distributions is introduced and their distribution functions and probability density functions are obtained. The moment generating functions of the quadratic forms in the skew normal variables are obtained. Sufficient and necessary conditions for the quadratic forms in the skew normal variables to have the noncentral generalized Dirichlet distributions are obtained. This leads to the noncentral Cochran's Theorem for the skew normal distribution.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Multivariate Analysis.
Volume (Year): 95 (2005)
Issue (Month): 2 (August)
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Branco, Márcia D. & Dey, Dipak K., 2001. "A General Class of Multivariate Skew-Elliptical Distributions," Journal of Multivariate Analysis, Elsevier, vol. 79(1), pages 99-113, October.
- Fang, B. Q., 2003. "The skew elliptical distributions and their quadratic forms," Journal of Multivariate Analysis, Elsevier, vol. 87(2), pages 298-314, November.
- Loperfido, Nicola, 2001. "Quadratic forms of skew-normal random vectors," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 381-387, October.
- Genton, Marc G. & He, Li & Liu, Xiangwei, 2001. "Moments of skew-normal random vectors and their quadratic forms," Statistics & Probability Letters, Elsevier, vol. 51(4), pages 319-325, February.
- A. Azzalini & A. Capitanio, 1999. "Statistical applications of the multivariate skew normal distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 579-602.
- Fang, B.Q., 2008. "Noncentral matrix quadratic forms of the skew elliptical variables," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1105-1127, July.
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