The rates of convergence for generalized entropy of the normalized sums   of IID random variables
  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. 
Hongfei Cui, Jianqiang Sun and Yiming Ding
cs.IT math.IT math.PR