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

Hongfei Cui; Jianqiang Sun; Yiming Ding

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arXiv · 1106.3381

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

Hongfei Cui·Jianqiang Sun·Yiming Ding

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Abstract

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

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Hongfei Cui, Jianqiang Sun, Yiming Ding. 2011-06-17. The rates of convergence for generalized entropy of the normalized sums of IID random variables. https://arxiv.org/abs/1106.3381

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