Entropy and Effective Support Size

Entropy

关键词: Rényi’s entropy;    Shannon’s entropy;    support;    interpretation;    Probability;    Statistics;   

DOI  :  10.3390/e8030169

来源: mdpi

【 摘 要 】

Notion of Effective size of support (Ess) of a random variable is introduced. A small set of natural requirements that a measure of Ess should satisfy is presented. The measure with prescribed properties is in a direct (exp-) relationship to the family of Rényi’s α-entropies which includes also Shannon’s entropy H. Considerations of choice of the value of α imply that exp(H) appears to be the most appropriate measure of Ess. Entropy and Ess can be viewed thanks to their log / exp relationship as two aspects of the same thing. In Probability and Statistics the Ess aspect could appear more basic than the entropic one.

【 授权许可】

Unknown   
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