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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
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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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 (CC BY 3.0).

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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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