Abstract
AbstractNonuniform estimates are obtained for Poisson, compound Poisson, translated Poisson, negative binomial and binomial approximations to sums of of m-dependent integer-valued random variables. Estimates for Wasserstein metric also follow easily from our results. The results are then exemplified by the approximation of Poisson binomial distribution, 2-runs and m-dependent \((k_1,k_2)\)-events.KeywordsPoisson distributionCompound Poisson distributionTranslated Poisson distributionNegative binomial distributionBinomial distribution M-dependent variablesWasserstein normNonuniform estimates.
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