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We study convexity properties of R\'{e}nyi entropy as function of $\alpha>0$on finite alphabets. We also describe robustness of the R\'{e}nyi entropy onfinite alphabets, and it turns out that the rate of respective convergencedepends on initial alphabet. We establish convergence of the disturbed entropywhen the initial distribution is uniform but the number of events increases to$\infty$ and prove that limit of R\'{e}nyi entropy of binomial distribution isequal to R\'{e}nyi entropy of Poisson distribution.

Convexity and robustness of the R\'{e}nyi entropy