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Accurate and asymptotic results for distributions of scan statistics

Published online by Cambridge University Press:  14 July 2016

D. J. Gates  and
M. Westcott
D. J. Gates*
Affiliation:
CSIRO Division of Mathematics and Statistics, Canberra
M. Westcott*
Affiliation:
CSIRO Division of Mathematics and Statistics, Canberra
*
∗Postal address: CSIRO Division of Mathematics and Statistics, P.O. Box 1965, Canberra City, ACT 2601, Australia.
∗Postal address: CSIRO Division of Mathematics and Statistics, P.O. Box 1965, Canberra City, ACT 2601, Australia.
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Abstract

We derive asymptotic forms for the distributions of k-point scan statistics as the interval L under study becomes infinite, while k and the window length are held fixed. In the Poisson case the intensity is also held fixed. In the uniform case the number of points N becomes infinite and N/L tends to a limit, representing a limiting intensity. These results are made explicit for k = 3, and in the Poisson case provide approximations which are typically accurate to six or seven figures, even for small L.

Keywords

ASYMPTOTIC DISTRIBUTIONINTEGRAL EQUATIONLAPLACE TRANSFORMSADDLEPOINT INTEGRATIONSTATISTICAL MECHANICS
Type
Research Papers
Information
Journal of Applied Probability , Volume 22 , Issue 3 , September 1985 , pp. 531 - 542
Copyright
Copyright © Applied Probability Trust 1985 

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