Quadratic forms of multivariate skew normal-symmetric distributions
Following the paper by Gupta and Chang (Multivariate skew-symmetric distributions. Appl. Math. Lett. 16, 643-646 2003.) we generate a multivariate skew normal-symmetric distribution with probability density function of the form fZ(z)=2[phi]p(z;[Omega])G([alpha]'z), where , [phi]p(z;[Omega]) is the p-dimensional normal p.d.f. with zero mean vector and correlation matrix [Omega], and G is taken to be an absolutely continuous function such that G' is symmetric about 0. First we obtain the moment generating function of certain quadratic forms. It is interesting to find that the distributions of some quadratic forms are independent of G. Then the joint moment generating functions of a linear compound and a quadratic form, and two quadratic forms, and conditions for their independence are given. Finally we take G to be one of normal, Laplace, logistic or uniform distribution, and determine the distribution of a special quadratic form for each case.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 76 (2006)
Issue (Month): 9 (May)
|Contact details of provider:|| Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description|
|Order Information:|| Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional|
References listed on IDEAS
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.:
- 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.
- Arjun Gupta & Truc Nguyen & Jose Sanqui, 2004. "Characterization of the skew-normal distribution," Annals of the Institute of Statistical Mathematics, Springer, vol. 56(2), pages 351-360, June.
- 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.
- Arnold, Barry C. & Beaver, Robert J., 2000. "The skew-Cauchy distribution," Statistics & Probability Letters, Elsevier, vol. 49(3), pages 285-290, September.
- Nadarajah, Saralees & Kotz, Samuel, 2003. "Skewed distributions generated by the normal kernel," Statistics & Probability Letters, Elsevier, vol. 65(3), pages 269-277, November.
- Gupta, Arjun K. & González-Farías, Graciela & Domínguez-Molina, J. Armando, 2004. "A multivariate skew normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 89(1), pages 181-190, April.
- Loperfido, Nicola, 2001. "Quadratic forms of skew-normal random vectors," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 381-387, October.
When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:76:y:2006:i:9:p:871-879. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.