Permanent URL to this publication: http://dx.doi.org/10.5167/uzh-22694
Roos, Malgorzata (1993). Compound Poisson approximations for the numbers of extreme spacings. Advances in Applied Probability, 25(4):847-874.
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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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|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
|Deposited On:||16 Nov 2009 12:33|
|Last Modified:||28 Nov 2013 00:32|
|Publisher:||Applied Probability Trust|
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