Abstract
In this paper three methods of the construction of approximations to generalized Poisson distributions are considered: approximation by a normal law, approximation by asymptotic distributions, the so-called Robbins mixtures, and approximation with the help of asymptotic expansions. Uniform and (for the first two methods) nonuniform estimates of the accuracy of the corresponding approximations are given. Some estimates for the concentration functions of generalized Poisson distributions are also presented.
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Supported by the Russian Foundation for Fundamental Research (grant No. 93-01-01446).
Proceedings of the XVII Seminar on Stability Problems for Stochastic Models, Kazan, Russia, 1995, Part II.
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Bening, V.E., Korolev, V.Y. & Shorgin, S.Y. On approximations to generalized Poisson distributions. J Math Sci 83, 360–373 (1997). https://doi.org/10.1007/BF02400920
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DOI: https://doi.org/10.1007/BF02400920