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

Kullback–Leibler Divergence Measure for Multivariate Skew-Normal Distributions

1,2,*  and 3
1 División de Investigación Pesquera, Instituto de Fomento Pesquero, Almte, Manuel Blanco Encalada 839, Valparaíso, 2361827, Chile 2 Departamento de Estadística, Universidad de Valparaíso, Gran Bretaña 1111, Playa Ancha, Valparaíso, 2360102, Chile 3 Departamento de Estadística, Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Av. Vicuña Mackenna 4860, Macul, Santiago, 7820436, Chile
* Author to whom correspondence should be addressed.
Received: 16 July 2012 / Revised: 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)
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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 (CC BY) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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

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