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Permanent URL to this publication: http://dx.doi.org/10.5167/uzh-22569

Barbour, A D; Chen, L; Choi, K (1995). Poisson approximation for unbounded functions. I. Independent summands. Statistica Sinica, 5(2):749-766.

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Abstract

Let , be independent random variables with such that as . Let and let be a Poisson random variable with mean . We obtain an absolute constant bound on , and using this, prove two Poisson approximation theorems for with unbounded and unrestricted. One of the theorems is then applied to obtain a large deviation result concerning for a general class of functions and again with unrestricted. The theorem is also applied to obtain an asymptotic result concerning ^_h((r-)/)|P(W_n=r)-P(Z=r)| for large