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Entropy 2012, 14(9), 1606-1626; doi:10.3390/e14091606
Article

Kullback–Leibler Divergence Measure for Multivariate Skew-Normal Distributions

1,2,*  and 3
Received: 16 July 2012; in revised form: 25 August 2012 / Accepted: 27 August 2012 / Published: 4 September 2012
(This article belongs to the Special Issue Distance in Information and Statistical Physics Volume 2)
Download PDF [2213 KB, uploaded 4 September 2012]
Abstract: The aim of this work is to provide the tools to compute the well-known Kullback–Leibler divergence measure for the flexible family of multivariate skew-normal distributions. In particular, we use the Jeffreys divergence measure to compare the multivariate normal distribution with the skew-multivariate normal distribution, showing that this is equivalent to comparing univariate versions of these distributions. Finally, we applied our results on a seismological catalogue data set related to the 2010 Maule earthquake. Specifically, we compare the distributions of the local magnitudes of the regions formed by the aftershocks.
Keywords: skew-normal; cross-entropy; Kullback–Leibler divergence; Jeffreys divergence; earthquakes; nonparametric clustering skew-normal; cross-entropy; Kullback–Leibler divergence; Jeffreys divergence; earthquakes; nonparametric clustering
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

Contreras-Reyes, J.E.; Arellano-Valle, R.B. Kullback–Leibler Divergence Measure for Multivariate Skew-Normal Distributions. Entropy 2012, 14, 1606-1626.

AMA Style

Contreras-Reyes JE, Arellano-Valle RB. Kullback–Leibler Divergence Measure for Multivariate Skew-Normal Distributions. Entropy. 2012; 14(9):1606-1626.

Chicago/Turabian Style

Contreras-Reyes, Javier E.; Arellano-Valle, Reinaldo B. 2012. "Kullback–Leibler Divergence Measure for Multivariate Skew-Normal Distributions." Entropy 14, no. 9: 1606-1626.


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