Maximizing Rényi entropy rate

Of all univariate distributions on the nonnegative reals of a given mean, the distribution that maximizes the Rényi entropy is Lomax. But the memoryless Lomax stochastic process does not maximize the Rényi entropy rate: For Rényi orders smaller than one the supremum of the Rényi entropy rates is...

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Bibliographic Details
Published in2014 IEEE 28th Convention of Electrical & Electronics Engineers in Israel (IEEEI) pp. 1 - 4
Main Authors Bunte, Christoph, Lapidoth, Amos
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.12.2014
Subjects
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Entropy
Joints
Probability density function
Random variables
Stochastic processes
Tin
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Summary:Of all univariate distributions on the nonnegative reals of a given mean, the distribution that maximizes the Rényi entropy is Lomax. But the memoryless Lomax stochastic process does not maximize the Rényi entropy rate: For Rényi orders smaller than one the supremum of the Rényi entropy rates is infinite, and for orders larger than one it is the differential Shannon entropy of the exponential distribution, which is the distribution that maximizes the differential Shannon entropy subject to these constraints. This is shown to be a special case of a much more general principle.
DOI:10.1109/EEEI.2014.7005859