Rare Events and Poisson Point Processes

The aim of the present work is to show that the results obtained earlier on the approximation of distributions of sums of independent terms by the accompanying compound Poisson laws may be interpreted as rather sharp quantitative estimates for the closeness between the sample containing independent...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2020-02, Vol.244 (5), p.771-778
Main Authors: Götze, F., Zaitsev, A. Yu
Format: Article
Language:English
Subjects:
Distribution (Probability theory)
Laws, regulations and rules
Mathematics
Mathematics and Statistics
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Summary:The aim of the present work is to show that the results obtained earlier on the approximation of distributions of sums of independent terms by the accompanying compound Poisson laws may be interpreted as rather sharp quantitative estimates for the closeness between the sample containing independent observations of rare events and the Poisson point process which is obtained after a Poissonization of the initial sample.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-020-04650-2