文章基本信息

标题：On magic factors in Stein’s method for compound Poisson approximation
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作者：Fraser Daly
期刊名称：Electronic Communications in Probability
印刷版ISSN：1083-589X
出版年度：2017
卷号：22
DOI：10.1214/17-ECP101
语种：English
出版社：Electronic Communications in Probability
摘要：One major obstacle in applications of Stein’s method for compound Poisson approximation is the availability of so-called magic factors (bounds on the solution of the Stein equation) with favourable dependence on the parameters of the approximating compound Poisson random variable. In general, the best such bounds have an exponential dependence on these parameters, though in certain situations better bounds are available. In this paper, we extend the region for which well-behaved magic factors are available for compound Poisson approximation in the Kolmogorov metric, allowing useful compound Poisson approximation theorems to be established in some regimes where they were previously unavailable. To illustrate the advantages offered by these new bounds, we consider applications to runs, reliability systems, Poisson mixtures and sums of independent random variables.
关键词：compound Poisson approximation;Stein’s method;Kolmogorov distance;runs; reliability.