In this short note, we develop a local approximation for the log-ratio of the multivariate hypergeometric probability mass function over the corresponding multinomial probability mass function. In conjunction with the bounds from Carter (2002) and Ouimet (2021) on the total variation between the law of a multinomial vector jittered by a uniform on $(-1/2,1/2)^d$ and the law of the corresponding multivariate normal distribution, the local expansion for the log-ratio is then used to obtain a total variation bound between the law of a multivariate hypergeometric random vector jittered by a uniform on $(-1/2,1/2)^d$ and the law of the corresponding multivariate normal distribution. As a corollary, we find an upper bound on the Le Cam distance between multivariate hypergeometric and multivariate normal experiments.

翻译：在此简短的注释中,我们为对应的多数值概率质量函数的多变量超几何概率值对数值值的对数近似值。结合卡特(2002年)和欧米特(2021年)关于由制服($-1/2/1/2)美元)和相应多变量正常分布法拼凑的多元矢量法总差异的界限,我们随后使用对数值的局部扩展来获得多变量超几何概率值随机矢量法与相应多变量正常分布法之间的总差异。作为必然结果,我们发现多变量超地球度和多变量正常实验之间的拉卡距离有上界。