# On the convergence of the Bhattacharyya bounds in the multiparametric case

Applicationes Mathematicae (1994)

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

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topAlharbi, 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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