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
@article{bwmeta1.element.bwnjournal-article-zmv22z3p339bwm,
author = {Abdulghani Alharbi},
title = {On the convergence of the Bhattacharyya bounds in the multiparametric case},
journal = {Applicationes Mathematicae},
volume = {22},
year = {1994},
pages = {339-349},
zbl = {0812.62056},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-zmv22z3p339bwm}
}
Alharbi, Abdulghani. On the convergence of the Bhattacharyya bounds in the multiparametric case. Applicationes Mathematicae, Tome 22 (1994) pp. 339-349. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-zmv22z3p339bwm/
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