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

Received: 5 May 2006; Accepted: 10 August 2006 / Published: 21 August 2006
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Abstract: 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 which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

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

AMA Style

Grendar M. Entropy and Effective Support Size. Entropy. 2006; 8(3):169-174.

Chicago/Turabian Style

Grendar, Marian. 2006. "Entropy and Effective Support Size." Entropy 8, no. 3: 169-174.


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