We present a method to approximate Rao's distance between multivariate normal distributions based on discretizing curves joining normal distributions and approximating Rao distances between successive nearby normals on the curve by using Jeffrey's divergence. We consider experimentally the linear interpolation curves in the ordinary, natural and expectation parameterizations of the normal distributions. We further consider a curve derived from the Calvo and Oller's isometric embedding of the Fisher-Rao $d$-variate normal manifold into the cone of $(d+1)\times (d+1)$ symmetric positive-definite matrices [Journal of multivariate analysis 35.2 (1990): 223-242]. Last, we present some information-geometric properties of the Calvo and Oller's mapping.

翻译：我们提出一种基于离散化连接正态分布的曲线，并利用Jeffrey散度近似曲线上连续邻近正态分布之间Rao距离的方法，来近似多变量正态分布之间的Rao距离。实验上，我们考虑了正态分布在普通、自然和期望参数化下的线性插值曲线。此外，我们还考虑了由Calvo和Oller提出的Fisher-Rao $d$元正态流形到$(d+1)\times (d+1)$对称正定矩阵锥的等距嵌入导出的曲线[Journal of multivariate analysis 35.2 (1990): 223-242]。最后，我们介绍了Calvo和Oller映射的一些信息几何性质。