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Bounds on the entropy series. (English) Zbl 0647.94006

Upper bounds on the entropy of a countable integer-valued random variable are furnished in terms of the expectation of the logarithm function. In particular, an upper bound is derived that is sharper than that of Elias, \(H(P)\leq E_ P(\log)+2(1+\sqrt{E_ P(\log)}),\) for all values of \(E_ P(\log)\). Bounds that are better only for large values of \(E_ P(\log)\) than the previous known upper bounds are also provided.

MSC:

94A17 Measures of information, entropy
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