A NON-UNIFORM BOUND ON
POISSON APPROXIMATION BY -FUNCTIONS

Abstract. The Stein-Chen method and -functions are used to give a result in the Poisson approximation to the distribution of a non-negative integer-valued random variable , in terms of the difference of cumulative distribution function of and Poisson cumulative distribution function together with its non-uniform bound. For applications, the result obtained in the present study is applied to approximate binomial, negative binomial, hypergeometric and negative hypergeometric cumulative distribution functions.

Received: June 24, 2012

AMS Subject Classification: 62E17, 60F05

Key Words and Phrases: cumulative distribution function, non-uniform bound, Poisson approximation, Stein's method; -functions

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