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http://dx.doi.org/10.5351/CKSS.2007.14.1.147

A Note Based on Multiparameter Discrete Exponential Families in View of Cacoullos-type Inequalities  

Borzadaran, G. R. Mohtashami (Department of Mathematics and Statistics Faculty of Science, University of Birjand)
Publication Information
Communications for Statistical Applications and Methods / v.14, no.1, 2007 , pp. 147-153 More about this Journal
Abstract
In this note, we obtained results related to multiparameter discrete exponential families on considering lattice or semi-lattice in place of N (Natural numbers) in view of Cacoullos-type inequalities via the same arguments in Papathanasiou (1990, 1993).
Keywords
Chernoff-type Inequalities; variance bounds; characterization; upper bounds; exponential families; lower bounds;
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1 Chen, L. H. Y. (1982). An inequality for the multivariate normal distribution. Journal of Multivariate Analysis, 12, 306-315   DOI
2 Chernoff, H. (1981). A note on an inequality involving the normal distribution. The Annals of Probability, 9, 533-535   DOI   ScienceOn
3 Kemp, A. W. (1997). Characterizations of a discrete normal distribution. Journal of Statistical Planning and Inference, 63, 223-229   DOI   ScienceOn
4 Klaassen, C. A. J. (1985). On an inequality of Chernoff. The Annals of Probability, 13, 966-974   DOI   ScienceOn
5 Koicheva, M. (1993). On an inequality and the related characterizations of the gamma distribution. Applications of Mathematics, 38, 11-18
6 Mohtashami Borzadaran, G. R. (2001). Characterization of Pearsonian and bilateral power series distribution via maximum entropies. Bayesian inference and maximum entropy methods in science and engineering, AlP Conference Proceedings, 568, 145-150
7 Mohtashami Borzadaran, G. R. and Shanbhag, D. N. (1998). Further results based on Chernofftype inequalities. Statistics & Probability Letters, 39, 109-117   DOI   ScienceOn
8 Cacoullos, T. (1982). On upper and lower bounds for the variance of a function of a random variable. Annals of Probability, 10,799-809   DOI   ScienceOn
9 Cacoullos, T. (1989). Dual Poincare-type inequalities via the Cramer-Rae and the CauchySchwarz inequalities and related characterizations. Statistical Data Analysis and Inference, Nortg-Holland, Amsterdam, 239-250
10 Cacoullos, T. and Papathanasiou, V. (1985). On upper bounds for the variance of functions of random variables. Statistics & Probability Letters, 3, 175-184   DOI   ScienceOn
11 Cacoullos, T. and Papathanasiou, V. (1989). Characterizations of distributions by variance bounds. Statistics & Probability Letters, 7, 351-356   DOI   ScienceOn
12 Cacoullos, T. and Papathanasiou, V. (1995). A generalization of covariance identity and related characterizations. Mathematical Methods of Statistics, 4, 106-113
13 Cacoullos, T. and Papathanasiou, V. (1997). Characterizations of distributions by generalizations of variance bounds and simple proofs of the CLT. Journal of Statistical Planning and Inference, 63, 157-171   DOI   ScienceOn
14 Borovkov, A. A. and Utev, S. A. (1984). On an inequality and a related characterization of the normal distribution. Theory of Probability and its Applications, 28, 219-228   DOI
15 Papathanasiou, V. (1990). Characterizations of multidimensional exponential families by Cacoullos-type inequalities. Journal of Multivariate Analysis, 35, 102-107   DOI
16 Cacoullos, T. and Papathanasiou, V. (1986). Bounds for the variance of functions of random variables by orthogonal polynomial and Bhattacharyya bounds. Statistics & Probability Letters, 4, 21-23   DOI   ScienceOn
17 Alharbi, A. A. and Shanbhag, D. N. (1996). General characterization theorems based on versions of the Chernoff inequality and the Cox representation. Journal of Statistical Planning and Inference, 55, 139-150   DOI   ScienceOn
18 Papathanasiou, V. (1993). Some characteristic properties of the Fisher information matrix via Cacoullos-type inequalities. Journal of Multivariate Analysis, 44, 256-265   DOI   ScienceOn