On Stein's method, smoothing estimates in total variation distance and mixture distributions |
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Authors: | Fraser Daly |
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Institution: | Heilbronn Institute for Mathematical Research, Department of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK |
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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. |
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Keywords: | Total variation distance Stein's method Mixed Poisson distribution Mixed binomial distribution Pó lya distribution Translated Poisson approximation Compound Poisson approximation |
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