  We consider the generalized differential entropy of normalized sums of
independent and identically distributed (IID) continuous random variables. We
prove that the R\'{e}nyi entropy and Tsallis entropy of order $\alpha\
(\alpha>0)$ of the normalized sum of IID continuous random variables with
bounded moments are convergent to the corresponding R\'{e}nyi entropy and
Tsallis entropy of the Gaussian limit, and obtain sharp rates of convergence.
