We study the dually flat information geometry of the Tojo-Yoshino exponential family with has sample space the Poincar\'e upper plane and parameter space the open convex cone of $2\times 2$ symmetric positive-definite matrices. Using the framework of Eaton's maximal invariant, we prove that all $f$-divergences between Tojo-Yoshino Poincar\'e distributions are functions of $3$ simple determinant/trace terms. We report closed-form formula for the Fisher information matrix, the differential entropy and the Kullback-Leibler divergence and Bhattacharyya distance between such distributions.

翻译：我们研究了东京-横野指数式家族的双平式信息几何方法,其样本空间为Poincar\'e上方平面和参数空间,开放的锥形锥体为2美元乘以2美元对称正-确定矩阵。我们利用Eaton最大变数框架,证明Tojo-Yoshino Poincar\'e分布之间的所有美元差异都是3美元简单的决定因素/跟踪术语的函数。我们报告了Fisher信息矩阵的闭式公式、差宽的英式和Kullback-Leiber差异以及这些分布之间的巴塔恰里雅距离。