## Abstract

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 |
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Original language | English |

Pages (from-to) | 2228 - 2237 |

Number of pages | 10 |

Journal | Journal of statistical planning and inference |

Volume | 141 |

Issue number | 7 |

DOIs | |

Publication status | Published - Jul 2011 |