On the symmetrized \(s\)-divergence. (English) Zbl 1443.60029
Summary: In this study, we work with the relative divergence of type \(s\), \(s\in{\mathbb{R}}\), which includes the Kullback-Leibler divergence and the Hellinger and \(\chi^2\) distances as particular cases. We study the symmetrized divergences in additive and multiplicative forms. Some basic properties such as symmetry, monotonicity and log-convexity are established. An important result from the convexity theory is also proved.
MSC:
| 60E15 | Inequalities; stochastic orderings |
References:
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