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Compound Poisson approximations for the numbers of extreme spacings


Roos, Malgorzata (1993). Compound Poisson approximations for the numbers of extreme spacings. Advances in Applied Probability, 25(4):847-874.

Abstract

The accuracy of the Poisson approximation to the distribution of the numbers of large and small m-spacings, when n points are placed at random on the circle, was
analysed using the Stein-Chen method in Barbour et al. (1992b). The Poisson approximation for m _ 2 was found not to be as good as for 1-spacings. In this paper, rates of approximation of these distributions to suitable compound Poisson distributions are worked out, using the CP-Stein-Chen method and an appropriate coupling argument. The rates are better than for Poisson approximation for m ' 2, and are of order O((log n)2/n) for large m-spacings and of order 0(1/n) for small m-spacings, for any fixed m > 2, if the expected number of spacings is held constant as n - oo.

Abstract

The accuracy of the Poisson approximation to the distribution of the numbers of large and small m-spacings, when n points are placed at random on the circle, was
analysed using the Stein-Chen method in Barbour et al. (1992b). The Poisson approximation for m _ 2 was found not to be as good as for 1-spacings. In this paper, rates of approximation of these distributions to suitable compound Poisson distributions are worked out, using the CP-Stein-Chen method and an appropriate coupling argument. The rates are better than for Poisson approximation for m ' 2, and are of order O((log n)2/n) for large m-spacings and of order 0(1/n) for small m-spacings, for any fixed m > 2, if the expected number of spacings is held constant as n - oo.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:04 Faculty of Medicine > Epidemiology, Biostatistics and Prevention Institute (EBPI)
07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:610 Medicine & health
510 Mathematics
Language:English
Date:1993
Deposited On:16 Nov 2009 12:33
Last Modified:05 Apr 2016 13:28
Publisher:Applied Probability Trust
ISSN:0001-8678
Publisher DOI:https://doi.org/10.2307/1427795
Official URL:http://www.jstor.org/stable/1427795

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