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.
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Bibliographic InfoArticle provided by Elsevier in its journal Statistics & Probability Letters.
Volume (Year): 69 (2004)
Issue (Month): 4 (October)
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