Poisson type approximations for the Markov binomial distribution |
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Authors: | Vydas Čekanavičius Bero Roos |
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Affiliation: | 1. Department of Mathematics and Informatics, Vilnius University, Naugarduko 24, Vilnius 03225, Lithuania;2. Department of Mathematics, University of Leicester, University Road, Leicester LE1 7RH, United Kingdom |
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Abstract: | The Markov binomial distribution is approximated by the Poisson distribution with the same mean, by a translated Poisson distribution and by two-parametric Poisson type signed measures. Using an adaptation of Le Cam’s operator technique, estimates of accuracy are proved for the total variation, local and Wasserstein norms. In a special case, asymptotically sharp constants are obtained. For some auxiliary results, we used Stein’s method. |
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Keywords: | primary, 60J10 secondary, 60F05 |
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