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Title

On the convergence of the Bhattacharyya bounds in the multiparametric case

Authors 1

Affiliations

  1. Department of Physics & Mathematics, University of King Abdulaziz, P.O. Box 344, Madinah Munawwarah, Saudi Arabia

Abstract

Shanbhag (1972, 1979) showed that the diagonality of the Bhattacharyya matrix characterizes the set of normal, Poisson, binomial, negative binomial, gamma or Meixner hypergeometric distributions. In this note, using Shanbhag's techniques, we show that if a certain generalized version of the Bhattacharyya matrix is diagonal, then the bivariate distribution is either normal, Poisson, binomial, negative binomial, gamma or Meixner hypergeometric. Bartoszewicz (1980) extended the result of Blight and Rao (1974) to the multiparameter case. He gave an application of this result when independent samples come from the exponential distribution, and also evaluated the generalized Bhattacharyya bounds for the best unbiased estimator of P(Y

Keywords

ENG
exponential family, characterizations, Seth-Shanbhag results, bivariate distributions, MVUE, Bhattacharyya bounds, diagonal of covariance matrix

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Applicationes Mathematicae
1993-1995/22/3
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Pages:
339-349
Main language of publication
English
Received
1993-06-14
Accepted
1993-11-26
Published
1994
Exact and natural sciences