Bernoulli

Sharp estimates in signed Poisson approximation of Poisson mixtures

José Antonio Adell and Alberto Lekuona

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Abstract

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.

Article information

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

Dates
First available: 7 March 2005

Permanent link to this document
http://projecteuclid.org/euclid.bj/1110228242

Mathematical Reviews number (MathSciNet)
MR2121455

Digital Object Identifier
doi:10.3150/bj/1110228242

Zentralblatt MATH identifier
1062.60034

Citation

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. http://projecteuclid.org/euclid.bj/1110228242.


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References

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