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

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

2010-11-26

arxiv.org/abs/1011.5734v1

Bernoulli 2010, Vol. 16, No. 4, 1114-1136

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.3150/09-BEJ246 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

10.3150/09-BEJ246

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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