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

  • Published : 2007.04.30

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

References

  1. 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 https://doi.org/10.1016/0378-3758(95)00191-3
  2. 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 https://doi.org/10.1137/1128021
  3. Cacoullos, T. (1982). On upper and lower bounds for the variance of a function of a random variable. Annals of Probability, 10,799-809 https://doi.org/10.1214/aop/1176993788
  4. 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
  5. Cacoullos, T. and Papathanasiou, V. (1985). On upper bounds for the variance of functions of random variables. Statistics & Probability Letters, 3, 175-184 https://doi.org/10.1016/0167-7152(85)90014-8
  6. 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 https://doi.org/10.1016/0167-7152(86)90033-7
  7. Cacoullos, T. and Papathanasiou, V. (1989). Characterizations of distributions by variance bounds. Statistics & Probability Letters, 7, 351-356 https://doi.org/10.1016/0167-7152(89)90050-3
  8. Cacoullos, T. and Papathanasiou, V. (1995). A generalization of covariance identity and related characterizations. Mathematical Methods of Statistics, 4, 106-113
  9. 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 https://doi.org/10.1016/S0378-3758(97)00008-6
  10. Chen, L. H. Y. (1982). An inequality for the multivariate normal distribution. Journal of Multivariate Analysis, 12, 306-315 https://doi.org/10.1016/0047-259X(82)90022-7
  11. Chernoff, H. (1981). A note on an inequality involving the normal distribution. The Annals of Probability, 9, 533-535 https://doi.org/10.1214/aop/1176994428
  12. Kemp, A. W. (1997). Characterizations of a discrete normal distribution. Journal of Statistical Planning and Inference, 63, 223-229 https://doi.org/10.1016/S0378-3758(97)00020-7
  13. Klaassen, C. A. J. (1985). On an inequality of Chernoff. The Annals of Probability, 13, 966-974 https://doi.org/10.1214/aop/1176992917
  14. Koicheva, M. (1993). On an inequality and the related characterizations of the gamma distribution. Applications of Mathematics, 38, 11-18
  15. 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
  16. Mohtashami Borzadaran, G. R. and Shanbhag, D. N. (1998). Further results based on Chernofftype inequalities. Statistics & Probability Letters, 39, 109-117 https://doi.org/10.1016/S0167-7152(98)00036-4
  17. Papathanasiou, V. (1990). Characterizations of multidimensional exponential families by Cacoullos-type inequalities. Journal of Multivariate Analysis, 35, 102-107 https://doi.org/10.1016/0047-259X(90)90018-D
  18. Papathanasiou, V. (1993). Some characteristic properties of the Fisher information matrix via Cacoullos-type inequalities. Journal of Multivariate Analysis, 44, 256-265 https://doi.org/10.1006/jmva.1993.1014