Sankhya: The Indian Journal of Statistics
2003, Volume 65, Pt. 2, 284--291
Constancy Of Regressions For Beta Distributions
VANAMAMALAI SESHADRI, McGill University, Montreal, Canada and JACEK WESO\L OWSKI, Politechnika Warszawska, Warsaw, Poland
SUMMARY: Properties of preserving independence under some transformations are known to characterize such important families of distributions as normal, exponential, gamma, Cauchy, uniform, (generalized) inverse Gaussian. Recently, a similar type of result of such a shape for the beta distribution has been proved in Weso\l owski (2002a). In the present paper related characterizations of beta laws are obtained under weaker conditions of constancy of regressions.
AMS (1991) subject classification. 60E05, 62E10.
Key words and phrases. Backward martingale, beta distribution, characterizations of probability distributions, constancy of regression, Dirichlet distribution, independence, moments method.