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Entropy 2016, 18(8), 278; doi:10.3390/e18080278

Expected Logarithm of Central Quadratic Form and Its Use in KL-Divergence of Some Distributions

1
School of Electrical and Computer Engineering, College of Engineering, University of Tehran, P.O. Box 14395-515, Tehran, Iran
2
School of Computer Science, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran
*
Author to whom correspondence should be addressed.
Academic Editor: Raúl Alcaraz Martínez
Received: 10 May 2016 / Revised: 13 July 2016 / Accepted: 21 July 2016 / Published: 28 July 2016
(This article belongs to the Section Information Theory)
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Abstract

In this paper, we develop three different methods for computing the expected logarithm of central quadratic forms: a series method, an integral method and a fast (but inexact) set of methods. The approach used for deriving the integral method is novel and can be used for computing the expected logarithm of other random variables. Furthermore, we derive expressions for the Kullback–Leibler (KL) divergence of elliptical gamma distributions and angular central Gaussian distributions, which turn out to be functions dependent on the expected logarithm of a central quadratic form. Through several experimental studies, we compare the performance of these methods. View Full-Text
Keywords: expected logarithm; central quadratic form; Kullback–Leibler divergence; entropy; angular central Gaussian; elliptical gamma expected logarithm; central quadratic form; Kullback–Leibler divergence; entropy; angular central Gaussian; elliptical gamma
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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. (CC BY 4.0).

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Habib Zadeh, P.; Hosseini, R. Expected Logarithm of Central Quadratic Form and Its Use in KL-Divergence of Some Distributions. Entropy 2016, 18, 278.

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