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

The rates of convergence for generalized entropy of the normalized sums of IID random variables