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The rates of convergence for generalized entropy of the normalized sums of IID random variables (1106.3381v1)
Published 17 Jun 2011 in cs.IT, math.IT, and math.PR
Abstract: 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.