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Divergences or similarity measures between probability distributions havebecome a very useful tool for studying different aspects of statistical objectssuch as time series, networks and images. Notably not every divergence providesidentical results when applied to the same problem. Therefore it is convenientto have the widest possible set of divergences to be applied to the problemsunder study. Besides this choice an essential step in the analysis of everystatistical object is the mapping of each one of their representing values intoan alphabet of symbols conveniently chosen. In this work we attack bothproblems, that is, the choice of a family of divergences and the way to do themap into a symbolic sequence. For advancing in the first task we work with thefamily of divergences known as the Burbea-Rao centroids (BRC) and for thesecond one we proceed by mapping the original object into a symbolic sequencethrough the use of ordinal patterns. Finally we apply our proposals to analysesimulated and real time series and to real textured images. The main conclusionof our work is that the best BRC, at least in the studied cases, is the JensenShannon divergence, besides the fact that it verifies some interesting formalproperties.

Rao-Burbea centroids applied to the statistical characterisation of time series and images through ordinal patterns