It is well-known that the Bhattacharyya, Hellinger, Kullback-Leibler, $\alpha$-divergences, and Jeffreys' divergences between densities belonging to a same exponential family have generic closed-form formulas relying on the strictly convex and real-analytic cumulant function characterizing the exponential family. In this work, we report (dis)similarity formulas which bypass the explicit use of the cumulant function and highlight the role of quasi-arithmetic means and their multivariate mean operator extensions. In practice, these cumulant-free formulas are handy when implementing these (dis)similarities using legacy Application Programming Interfaces (APIs) since our method requires only to partially factorize the densities canonically of the considered exponential family.

翻译：众所周知,Bhattacharyya、Hellinger、Kullback-Leiber、$\alpha$-diverences和Jeffreys属于同一指数家族的密度差异之间有通用的封闭式公式,这些公式依赖纯粹的 convex 和真实分析的累积功能,以指数家族为特征。在这项工作中,我们报告(不同的)差异式公式,这些公式绕过对累积函数的明确使用,并突出准定量手段的作用及其多变量操作员平均扩展。 实际上,这些累积式公式在实施这些(不同)差异时,使用传统应用方案接口(APIs)是方便的,因为我们的方法只需要部分地将被视为指数型家庭的密度因素化。