Sankhya: The Indian Journal of Statistics

2001, Volume 63, Series A, Pt. 1, pp.113--117



G.R. MOHTASHAMI BORZADARAN, University of Birjand, Birjand, Iran

SUMMARY. In this paper, we consider characterizations based on the Bhattacharyya matrices. We begin the paper by obtaining the structure of the rth moment of the random variable X about the origin for a natural exponential family when the variance is a polynomial of the mean such that the mean is a linear function of the parameter of the family. We also characterize, under certain constraints, distributions such as normal, compound Poisson and gamma via the diagonality of the 2X2 Bhattacharyya matrix.

AMS (1991) subject classification. Primary 62E10, 62H10; secondary 60E05.

Key words and phrases. Exponential families, Seth-Shanbhag-Morris theorems, Bhattacharyya bounds, Rao-Cramer inequality, Fisher information, diagonality of the Bhattacharyya matrices.

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