The aim of this paper is to extend Stein's method to a compound Poisson distribution setting. The compound Poisson distributions of concern here are those of the form POIS(ν), where ν is a finite positive measure on (0, ∞). A number of results related to these distributions are established. These in turn are used in a number of examples to give bounds for the error in the compound Poisson approximation to the distribution of a sum of random variables.
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Barbour et al. (1992) studied this question.
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