Poisson Approximation for Unbounded Functions , I : Independent Summands

@inproceedings{Barbour1999PoissonAF,
  title={Poisson Approximation for Unbounded Functions , I : Independent Summands},
  author={Andrew D. Barbour and Louis H. Y. Chen and Kwok Pui Choi},
  year={1999}
}
Let Xn1; : : : ; Xnn; n 1; be independent random variables with P (Xni = 1) = 1 P (Xni = 0) = pni such that maxfpni : 1 i ng ! 0 as n ! 1: Let Wn = P 1 k n Xnk and Z be a Poisson random variable with mean = EWn. We obtain an absolute constant bound on P (Wn = r)=P (Z = r); r = 0; 1; : : : ; and using this, prove two Poisson approximation theorems for Eh(Wn) with h unbounded and unrestricted. One of the theorems is then applied to obtain a large deviation result concerning Eh(Wn)I(Wn z) for a… CONTINUE READING

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