Partial monotonicity of entropy measures
AbstractThe quantification of entropy has prominence in a diverse range of fields of study including information theory, quantum mechanics, thermodynamics, ecology, evolutionary biology and even sociology. Suppose we interpret the entropy of a random object as a measurement of the uncertainty about its outcome. This measurement is expected to decrease when the object’s outcome is confined into a shrinking interval. Entropies conforming to this intuition are thus sensible and likely useful measures of uncertainty. In this paper, we give a necessary and sufficient condition for the Shannon entropy of an absolutely continuous random variable to be an increasing function of the interval. Similar results are also obtained for the Renyi entropy of absolutely continuous random variables and their convolution.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Elsevier in its journal Statistics & Probability Letters.
Volume (Year): 82 (2012)
Issue (Month): 11 ()
Contact details of provider:
Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Bagnoli, M. & Bergstrom, T., 1989.
"Log-Concave Probability And Its Applications,"
89-23, Michigan - Center for Research on Economic & Social Theory.
- Burdett, Kenneth, 1996. "Truncated means and variances," Economics Letters, Elsevier, vol. 52(3), pages 263-267, September.
- Chen, Jiahua & van Eeden, Constance & Zidek, James, 2010. "Uncertainty and the conditional variance," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1764-1770, December.
- Gupta, Nitin & Bajaj, Rakesh Kumar, 2013. "On partial monotonic behaviour of some entropy measures," Statistics & Probability Letters, Elsevier, vol. 83(5), pages 1330-1338.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.