This note presents a refined local approximation for the logarithm of the ratio between the negative multinomial probability mass function and a multivariate normal density, both having the same mean-covariance structure. This approximation, which is derived using Stirling's formula and a meticulous treatment of Taylor expansions, yields an upper bound on the Hellinger distance between the jittered negative multinomial distribution and the corresponding multivariate normal distribution. Upper bounds on the Le Cam distance between negative multinomial and multivariate normal experiments ensue.

翻译：本文提出了一种关于负多项概率质量函数与具有相同均值-协方差结构的多元正态密度之比的精细局部近似。该近似通过使用斯特林公式以及对泰勒展开的细致处理推导得出，从而对抖动后的负多项分布与对应多元正态分布之间的海林格距离给出了上界。进而导出了负多项实验与多元正态实验之间勒卡姆距离的上界。