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On characterizations of the gamma and generalized inverse Gaussian distributions

Author

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  • Chou, Chao-Wei
  • Huang, Wen-Jang

Abstract

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.

Suggested Citation

  • Chou, Chao-Wei & Huang, Wen-Jang, 2004. "On characterizations of the gamma and generalized inverse Gaussian distributions," Statistics & Probability Letters, Elsevier, vol. 69(4), pages 381-388, October.
  • Handle: RePEc:eee:stapro:v:69:y:2004:i:4:p:381-388
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
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    Cited by:

    1. Wesołowski, Jacek, 2015. "On the Matsumoto–Yor type regression characterization of the gamma and Kummer distributions," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 145-149.
    2. Nadarajah, Saralees, 2009. "An alternative inverse Gaussian distribution," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(5), pages 1721-1729.

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