On the convergence of the Bhattacharyya bounds in the multiparametric case

Abdulghani Alharbi

Applicationes Mathematicae (1994)

  • Volume: 22, Issue: 3, page 339-349
  • ISSN: 1233-7234

Abstract

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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

How to cite

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Alharbi, Abdulghani. "On the convergence of the Bhattacharyya bounds in the multiparametric case." Applicationes Mathematicae 22.3 (1994): 339-349. <http://eudml.org/doc/219100>.

@article{Alharbi1994,
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},
author = {Alharbi, Abdulghani},
journal = {Applicationes Mathematicae},
keywords = {exponential family; characterizations; Seth-Shanbhag results; bivariate distributions; MVUE; Bhattacharyya bounds; diagonal of covariance matrix; diagonality; Bhattacharyya matrix; Meixner hypergeometric distributions; bivariate distribution; normal; Poisson; binomial; negative binomial; gamma; exponential distribution; generalized Bhattacharyya bounds; best unbiased estimator; minimum variance unbiased estimator; geometric distribution},
language = {eng},
number = {3},
pages = {339-349},
title = {On the convergence of the Bhattacharyya bounds in the multiparametric case},
url = {http://eudml.org/doc/219100},
volume = {22},
year = {1994},
}

TY - JOUR
AU - Alharbi, Abdulghani
TI - On the convergence of the Bhattacharyya bounds in the multiparametric case
JO - Applicationes Mathematicae
PY - 1994
VL - 22
IS - 3
SP - 339
EP - 349
AB - 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
LA - eng
KW - exponential family; characterizations; Seth-Shanbhag results; bivariate distributions; MVUE; Bhattacharyya bounds; diagonal of covariance matrix; diagonality; Bhattacharyya matrix; Meixner hypergeometric distributions; bivariate distribution; normal; Poisson; binomial; negative binomial; gamma; exponential distribution; generalized Bhattacharyya bounds; best unbiased estimator; minimum variance unbiased estimator; geometric distribution
UR - http://eudml.org/doc/219100
ER -

References

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  21. H. Tong (1974), A note on the estimation of Pr{Y<X} in the exponential case, Technometrics 16, 625. 
  22. H. Tong (1975), Errata: A note on the estimation of Pr{Y<X} in the exponential case, ibid. 17, 395. 

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