  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.
