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Entropy 2006, 8(3), 169-174; doi:10.3390/e8030169

Entropy and Effective Support Size

Department of Mathematics, FPV UMB, Tajovskeho 40, 974 01 Banska Bystrica, Slovakia Institute of Measurement Science, Bratislava, Slovakia Institute of Mathematics and Computer Science, Banska Bystrica, Slovakia
Received: 5 May 2006 / Accepted: 10 August 2006 / Published: 21 August 2006
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Notion of Effective size of support (Ess) of a random variable is introduced. A smallset of natural requirements that a measure of Ess should satisfy is presented. The measure withprescribed properties is in a direct (exp-) relationship to the family of R ́nyi’s α-entropies which eincludes 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 samething. In Probability and Statistics the Ess aspect could appear more basic than the entropic one.
Keywords: R´enyi’s entropy; Shannon’s entropy; support; interpretation; Probability; Statistics. R´enyi’s entropy; Shannon’s entropy; support; interpretation; Probability; Statistics.
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Grendar, M. Entropy and Effective Support Size. Entropy 2006, 8, 169-174.

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