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.
Publié le : 2010-11-15
Classification:
compound Poisson approximation,
geometric distribution,
local norm,
Markov binomial distribution,
signed compound Poisson measure,
total variation norm,
Wasserstein norm
@article{1290092898,
author = {\v Cekanavi\v cius, V. and Vellaisamy, P.},
title = {Compound Poisson and signed compound Poisson approximations to the Markov binomial law},
journal = {Bernoulli},
volume = {16},
number = {1},
year = {2010},
pages = { 1114-1136},
language = {en},
url = {http://dml.mathdoc.fr/item/1290092898}
}
Čekanavičius, V.; Vellaisamy, P. Compound Poisson and signed compound Poisson approximations to the Markov binomial law. Bernoulli, Tome 16 (2010) no. 1, pp. 1114-1136. http://gdmltest.u-ga.fr/item/1290092898/