Geodesic
Bounds on the information divergence for hypergeometric distributions
Kybernetika, Tome 56 (2020) no. 6, pp. 1111-1132
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The hypergeometric distributions have many important applications, but they have not had sufficient attention in information theory. Hypergeometric distributions can be approximated by binomial distributions or Poisson distributions. In this paper we present upper and lower bounds on information divergence. These bounds are important for statistical testing and for a better understanding of the notion of exchangeability.
The hypergeometric distributions have many important applications, but they have not had sufficient attention in information theory. Hypergeometric distributions can be approximated by binomial distributions or Poisson distributions. In this paper we present upper and lower bounds on information divergence. These bounds are important for statistical testing and for a better understanding of the notion of exchangeability.
DOI : 10.14736/kyb-2020-6-1111
Classification : 62E17, 94A17
Keywords: binomial distribution; hypergeometric distribution; information divergence; inequalities 
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Harremoës, Peter; Matúš, František. Bounds on the information divergence for hypergeometric distributions. Kybernetika, Tome 56 (2020) no. 6, pp. 1111-1132. doi: 10.14736/kyb-2020-6-1111

[1] Barbour, A. D., Holst, L., L., Janson, S.: Poisson Approximation. Oxford Studies in Probability 2, Clarendon Press, Oxford 1992. | DOI | MR

[2] Cover, T. M., Thomas, J. A.: Elements of Information Theory. Wiley Series in Telecommunications. 1991. | DOI | MR

[3] Csiszár, I., Shields, P.: Information Theory and Statistics: A Tutorial. Foundations and Trends in Communications and Information Theory, Now Publishers Inc., (2004) 4, 417-528. | DOI | MR

[4] Diaconis, P., Friedman, D.: A dozen de Finetti-style results in search of a theory. Ann. Inst. Henri Poincaré 23 (1987), 2, 397-423. | MR

[5] Harremoës, P.: Mutual information of contingency tables and related inequalities. In: 2014 IEEE International Symposium on Information Theory, IEEE 2014, pp. 2474-2478. | DOI

[6] Harremoës, P., Johnson, O., Kontoyiannis, I.: Thinning and information projections. arXiv:1601.04255, 2016. | MR

[7] Harremoës, P., Ruzankin, P.: Rate of Convergence to Poisson Law in Terms of Information Divergence. IEEE Trans. Inform Theory 50 (2004), 9, 2145-2149. | DOI | MR

[8] Matúš, F.: Urns and entropies revisited. In: 2017 IEEE International Symposium on Information Theory (ISIT) 2017, pp. 1451-1454. | DOI

[9] Stam, A. J.: Distance between sampling with and without replacement. Statistica Neerlandica 32 (1978), 2, 81-91. | DOI | MR

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