  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 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
$\infty$ and prove that limit of R\'{e}nyi entropy of binomial distribution is
equal to R\'{e}nyi entropy of Poisson distribution.
