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The paper gives the bounds on the solutions to a Stein equation for thenegative binomial distribution that are needed for approximation in terms ofthe Wasserstein metric. The proofs are probabilistic, and follow the approachintroduced in Barbour and Xia (Bernoulli 12 (2006) 943-954). The bounds areused to quantify the accuracy of negative binomial approximation to parasitecounts in hosts. Since the infectivity of a population can be expected to beproportional to its total parasite burden, the Wasserstein metric is theappropriate choice.

Stein factors for negative binomial approximation in Wasserstein distance