On characterizations of the gamma and generalized inverse Gaussian distributions
AbstractGiven two independent non-degenerate positive random variables X and Y, Letac and Wesolowski (Ann. Probab. 28 (2000) 1371) proved that U=(X+Y)-1 and V=X-1-(X+Y)-1 are independent if and only if X and Y are generalized inverse Gaussian (GIG) and gamma distributed, respectively. Note that X=(U+V)-1 and Y=U-1-(U+V)-1. This interesting transformation between (X,Y) and (U,V) preserves a bivariate probability measure which is a product of GIG and gamma distributions. In this work, characterizations of the GIG and gamma distributions through the constancy of regressions of Vr on U are considered.
Download InfoIf 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.
Bibliographic InfoArticle provided by Elsevier in its journal Statistics & Probability Letters.
Volume (Year): 69 (2004)
Issue (Month): 4 (October)
Contact details of provider:
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.:
- J. Pusz, 1997. "Regressional Characterization of the Generalized Inverse Gaussian Population," Annals of the Institute of Statistical Mathematics, Springer, vol. 49(2), pages 315-319, June.
- Shun-Hwa Li & Wen-Jang Huang & Mong-Na Huang, 1994. "Characterizations of the Poisson process as a renewal process via two conditional moments," Annals of the Institute of Statistical Mathematics, Springer, vol. 46(2), pages 351-360, June.
- Matsumoto, Hiroyuki & Yor, Marc, 2003. "Interpretation via Brownian motion of some independence properties between GIG and gamma variables," Statistics & Probability Letters, Elsevier, vol. 61(3), pages 253-259, February.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).
If references are entirely missing, you can add them using this form.