We present a simple method to approximate Rao's distance between multivariate normal distributions based on discretizing curves joining normal distributions and approximating Rao distances between successive nearby normal distributions on the curves by the square root of Jeffreys divergence. We consider experimentally the linear interpolation curves in the ordinary, natural and expectation parameterizations of the normal distributions, and compare these curves with 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]. We report on our experiments and assess the quality of our approximation technique by comparing the numerical approximations with lower and upper bounds. Finally, we present some information-geometric properties of the Calvo and Oller's isometric embedding.

翻译：我们提出一个简单的方法来接近拉奥的多变正常分布之间的距离,其依据是离散曲线连接正常分布和拉奥在曲线上相近正常分布之间的距离,以杰弗里的平方根为差分。我们实验地考虑了正常分布的普通、自然和预期参数化中的线性内插曲线,并将这些曲线与卡尔沃和奥尔勒的等分法将Fisher-Rao $d$-差分正方块嵌入(d+1)乘以(d+1)乘以(d+1)乘以(d)乘以(d+1)乘以(x)乘以正对正-断面矩阵[多变量分析杂志35.2(1990年):223-242]。我们通过比较卡尔沃和奥尔勒的直方形嵌入曲线的数值近似值与下限和上界比较,来报告我们的近似技术的质量。最后,我们介绍了卡尔沃和奥尔勒的直方块嵌入的一些信息几何特性。</s>