In many settings it is useful to have bounds on the total variation distance between some random variable Z and its shifted version Z+1. For example, such quantities are often needed when applying Stein's method for probability approximation. This note considers one way in which such bounds can be derived, in cases where Z is either the equilibrium distribution of some birth–death process or the mixture of such a distribution. Applications of these bounds are given to translated Poisson and compound Poisson approximations for Poisson mixtures and the Pólya distribution.
|Translated title of the contribution||On Stein's method, smoothing estimates in total variation distance and mixture distributions|
|Pages (from-to)||2228 - 2237|
|Number of pages||10|
|Journal||Journal of statistical planning and inference|
|Publication status||Published - Jul 2011|