On Stein-Chen factors for Poisson approximation

Timothy C. Brown and Aihua Xia

Statistics & Probability Letters, 1995, vol. 23, issue 4, 327-332

Abstract: The Stein-Chen method for the estimation of upper bounds of the distance of the whole distribution of a point process from that of a Poisson process was investigated in Barbour and Brown (1992). A feature of the Stein-Chen approximation for random variables is the existence of "magic" factors which decrease with the mean of the Poisson distribution. Using a Wasserstein metric for process approximation, one of these factors behaves in a similar way to that for random variables but the other involves an additional logarithm. Counterexamples are presented here to show that the logarithmic factor is necessary.

Keywords: Total; variation; distance; Point; process; Immigration-death; process; Stein-Chen; method (search for similar items in EconPapers)
Date: 1995
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Citations: View citations in EconPapers (1)

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