Sankhya: The Indian Journal of Statistics

2001, Volume 63, Series A, Pt. 1, pp.107--112

MUTUAL CHARACTERIZATIONS OF THE GAMMA AND THE GENERALIZED INVERSE GAUSSIAN LAWS BY CONSTANCY OF REGRESSION

By

VANAMAMALAI SESHADRI, McGill University, Montreal, Canada

and

JACEK WESOLOWSKI, Politechnika Warszawska, Warszawa, Poland

SUMMARY. Let X and Y be non-negative independent random variables. Characterizations of the generalized inverse Gaussian and gamma distributions through the constancy of regression of X-1 - (X+Y)-1 on X+Y are considered.

AMS (1991) subject classification. 60E05, 62E10.

Key words and phrases. Bessel equation, constancy of regression, characterizations of probability distributions, gamma distribution, generalized inverse Gaussian distribution.

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