Artículo de publicación ISIThe entropy and mutual information index are important concepts developed by Shannon in the context of information theory. They have been widely studied in the case of the multivariate normal distribution. We first extend these tools to the full symmetric class of multivariate elliptical distributions and then to the more flexible families of multivariate skew-elliptical distributions.We study in detail the cases of the multivariate skew-normal and skew-t distributions. We implement our findings to the application of the optimal design of an ozone monitoring station network in Santiago de Chile

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.

Communicated by Andras DerBiological-fishery indicators have been widely studied. As such the condition factor (CF) index, which interprets the fatness level of a certain species based on length and weight, has been investigated, too. However, CF has been studied without considering its temporal features and distribution. In this paper, we analyze the CF time series via skewgaussian distributions that consider the asymmetry produced by extreme events. This index is characterized by a threshold autoregressive model and corresponds to a stationary process depending on the shape parameter of the skew-gaussian distribution. Then we use the Jensen-Shannon (JS) distance to compare CF by length classes. This distance has mathematical advantages over other divergences such as Kullback-Leibler and Jeffrey's, and the triangular inequality property. Our results are applied to a biological catalogue of anchovy (Engraulis ringens) from the northern coast of Chile, for the period 1990-2010 that consider monthly CF time series by length classes and sex. We find that for high values of shape parameter, JS distance tends to be more sensible to detect discrepancies than Jeffrey's divergence. In addition, the body condition of male anchovies with higher lengths coincides with the ending of the moderate-strong El Niño event 91-92 and for both males and females, the smaller lengths coincide with the beginning of the strong El Niño event 97-98.