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Entropy 2012, 14(7), 1221-1233; doi:10.3390/e14071221

Nonparametric Estimation of Information-Based Measures of Statistical Dispersion

Institute of Physiology, Academy of Sciences of the Czech Republic, Videnska 1083, 142 20 Prague, Czech Republic
* Author to whom correspondence should be addressed.
Received: 29 March 2012 / Revised: 20 June 2012 / Accepted: 4 July 2012 / Published: 10 July 2012
(This article belongs to the Special Issue Concepts of Entropy and Their Applications)
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We address the problem of non-parametric estimation of the recently proposed measures of statistical dispersion of positive continuous random variables. The measures are based on the concepts of differential entropy and Fisher information and describe the “spread” or “variability” of the random variable from a different point of view than the ubiquitously used concept of standard deviation. The maximum penalized likelihood estimation of the probability density function proposed by Good and Gaskins is applied and a complete methodology of how to estimate the dispersion measures with a single algorithm is presented. We illustrate the approach on three standard statistical models describing neuronal activity.
Keywords: statistical dispersion; entropy; Fisher information; nonparametric density estimation statistical dispersion; entropy; Fisher information; nonparametric density estimation
This is an open access article distributed under the Creative Commons Attribution License (CC BY) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Kostal, L.; Pokora, O. Nonparametric Estimation of Information-Based Measures of Statistical Dispersion. Entropy 2012, 14, 1221-1233.

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