**Sankhya:
The Indian Journal of Statistics**

2003, Volume 65, Pt. 2, 284--291

**Constancy Of Regressions For Beta
Distributions**

By

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.