Next Article in Journal
Cosmology of F(T) Gravity and k-Essence
Next Article in Special Issue
Pushing for the Extreme: Estimation of Poisson Distribution from Low Count Unreplicated Data—How Close Can We Get?
Previous Article in Journal
Stability of Accelerating Cosmology in Two Scalar-Tensor Theory: Little Rip versus de Sitter
Previous Article in Special Issue
Geometry of q-Exponential Family of Probability Distributions
Article Menu

Export Article

Open AccessArticle
Entropy 2012, 14(9), 1606-1626;

Kullback–Leibler Divergence Measure for Multivariate Skew-Normal Distributions

División de Investigación Pesquera, Instituto de Fomento Pesquero, Almte, Manuel Blanco Encalada 839, Valparaíso, 2361827, Chile
Departamento de Estadística, Universidad de Valparaíso, Gran Bretaña 1111, Playa Ancha, Valparaíso, 2360102, Chile
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)
Full-Text   |   PDF [2213 KB, uploaded 24 February 2015]   |  


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. View Full-Text
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

Figure 1

This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

Share & Cite This Article

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.

Show more citation formats Show less citations formats

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top