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

2011/06/17 by Hongfei Cui, Jianqiang Sun, Cui, Hongfei +3
Computer Science · Engineering · Mathematics · Physics and Astronomy · #62B10 #94A17 #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Probability (math.PR) #Statistical Distribution Estimation and Applications #Statistical Mechanics and Entropy #Wireless Communication Security Techniques #cs.IT #math.IT #math.PR #msc:62B10 #msc:94A17

paper · pdf · doi:10.48550/arxiv.1106.3381

7 pages

arxiv created 2011/06/17 · openalex publication_date 2011/06/17 · arxiv updated 2011/06/20 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

Citations

• Generalized Entropy Power Inequalities and Monotonicity Properties of Information

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