Sharp estimates in signed Poisson approximation of Poisson mixtures

José Antonio Adell and Alberto Lekuona

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We give sharp estimates in total variation and certain kinds of stop-loss metrics in signed Poisson approximation of Poisson mixtures. We provide closed-form solutions to the problem of best choice of the Poisson parameter in simple Poisson approximation with respect to the total variation distance. The important special case of the negative binomial distribution is also discussed. To obtain our results, we apply a differential calculus based on different Taylor formulae for the Poisson process which allows us to give simple unified proofs.

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Bernoulli Volume 11, Number 1 (2005), 47-65.

First available in Project Euclid: 7 March 2005

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Charlier polynomials finite signed measure Poisson approximation Poisson mixture probability metrics


Antonio Adell, José; Lekuona, Alberto. Sharp estimates in signed Poisson approximation of Poisson mixtures. Bernoulli 11 (2005), no. 1, 47--65. doi:10.3150/bj/1110228242.

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