On characterizations of the gamma and generalized inverse Gaussian distributions
Given 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.
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|
|Order Information:|| Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional|
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.:
- 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.
- J. Pusz, 1997. "Regressional Characterization of the Generalized Inverse Gaussian Population," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, 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;The Institute of Statistical Mathematics, vol. 46(2), pages 351-360, June.
When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:69:y:2004:i:4:p:381-388. See general information about how to correct material in RePEc.
If references are entirely missing, you can add them using this form.