Bernoulli

  • Bernoulli
  • Volume 16, Number 4 (2010), 1114-1136.

Compound Poisson and signed compound Poisson approximations to the Markov binomial law

V. Čekanavičius and P. Vellaisamy

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Abstract

Compound Poisson distributions and signed compound Poisson measures are used for approximation of the Markov binomial distribution. The upper and lower bound estimates are obtained for the total variation, local and Wasserstein norms. In a special case, asymptotically sharp constants are calculated. For the upper bounds, the smoothing properties of compound Poisson distributions are applied. For the lower bound estimates, the characteristic function method is used.

Article information

Source
Bernoulli, Volume 16, Number 4 (2010), 1114-1136.

Dates
First available in Project Euclid: 18 November 2010

Permanent link to this document
https://projecteuclid.org/euclid.bj/1290092898

Digital Object Identifier
doi:10.3150/09-BEJ246

Mathematical Reviews number (MathSciNet)
MR2759171

Zentralblatt MATH identifier
1213.60033

Keywords
compound Poisson approximation geometric distribution local norm Markov binomial distribution signed compound Poisson measure total variation norm Wasserstein norm

Citation

Čekanavičius, V.; Vellaisamy, P. Compound Poisson and signed compound Poisson approximations to the Markov binomial law. Bernoulli 16 (2010), no. 4, 1114--1136. doi:10.3150/09-BEJ246. https://projecteuclid.org/euclid.bj/1290092898


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