Gamma-Divergence. An Introduction to New Divergence Family

Divergences have become a very useful tool for measuring similarity (or dissimilarity) between probability distributions. Depending on the field of application, a more appropriate measure may be necessary. In this paper we introduce a family of divergences called γ-Divergences. They are based on the convexity property of the functions that generate them. We demonstrate that these divergences verify all the usually required properties, and we extend them to weighted probability distribution. In addition, we define a generalised entropy closely related to the γ-Divergences. Finally, we apply our findings to the analysis of simulated and real time series.