Convexity and robustness of the R\'enyi entropy
Abstract
We study convexity properties of R\'enyi entropy as function of α>0 on finite alphabets. We also describe robustness of the R\'enyi entropy on finite alphabets, and it turns out that the rate of respective convergence depends on initial alphabet. We establish convergence of the disturbed entropy when the initial distribution is uniform but the number of events increases to ∞ and prove that limit of R\'enyi entropy of binomial distribution is equal to R\'enyi entropy of Poisson distribution.
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