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Upper and lower bounds for Csiszár \(f\)-divergence in terms of Hellinger discrimination and applications. (English) Zbl 1028.94019

Summary: We point out an upper and a lower bound for the Csiszár \(f\)-divergence of two discrete random variables in terms of the Hellinger discrimination. Some particular cases for the Kullback-Leibler distance, triangular discrimination, \(\chi^2\)-distance and the Rényi \(\alpha\)-entropy, etc. are considered.

MSC:

94A17 Measures of information, entropy
26D15 Inequalities for sums, series and integrals
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