Stein factor bounds for random variables (Q2725319)

In applying Stein's method to approximate the distribution of a discrete random variable, an essential ingredient is to find tight bounds -- `magic factors' -- on the differences of the functions solving an associated Stein equation. For any approximating distribution on the nonnegative integers, a Stein equation can be derived by way of the generator of a suitably chosen birth and death process. Under very mild conditions on the approximating distribution, a general expression for the corresponding magic factors is determined. It is further shown to yield the best known factors in previously explored cases such as the Poisson distribution. The method of proof is based on ideas introduced by \textit{A. Xia} [J. Appl. Probab. 36, No. 1, 287-290 (1999; Zbl 0942.60006)].