The work deals with a special case of approximation with the Poisson distribution. Namely, it focuses on the sums of independent indicators, which have a hard-to-calculate distribution if the indicators are not uniformly distributed. We derive an explicit upper bound for the approximation error using the Chen–Stein method and the distance in the Wasserstein metric.
As a criterion for the deviation of the distribution of the random variable X from the better-known distribution of the random variable Y, we set the difference of the expected values of the functions from the suitable test class. We express this difference as the so-called Chen–Stein expected value: it is equal to exactly zero when the random variable X has the corresponding Poisson distribution. However, if the Chen–Stein expected value is small,
the deviation from the Poisson distribution is consequently also small.
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