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November 2010 Compound Poisson and signed compound Poisson approximations to the Markov binomial law
V. Čekanavičius, P. Vellaisamy
Bernoulli 16(4): 1114-1136 (November 2010). DOI: 10.3150/09-BEJ246

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.

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V. Čekanavičius. P. Vellaisamy. "Compound Poisson and signed compound Poisson approximations to the Markov binomial law." Bernoulli 16 (4) 1114 - 1136, November 2010. https://doi.org/10.3150/09-BEJ246

Information

Published: November 2010
First available in Project Euclid: 18 November 2010

zbMATH: 1213.60033
MathSciNet: MR2759171
Digital Object Identifier: 10.3150/09-BEJ246

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

Rights: Copyright © 2010 Bernoulli Society for Mathematical Statistics and Probability

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Vol.16 • No. 4 • November 2010
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