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Biometrika 1965 52(1-2):67-77; doi:10.1093/biomet/52.1-2.67
© 1965 by Biometrika Trust
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Some results on tests for Poisson processes

PETER A. W. LEWIS

IBM Research Laboratories, San Jose, California and Birkbeck College, University of London

It is shown that a test proposed by Barnard for Poisson processes, using certain distributionfree statistics, is not consistent against renewal alternatives. However, empirical evidence is given which suggests that a modification of this test due to Durbin results in relatively powerful tests of the Poisson hypothesis. A simple test based on Durbin's modification is described, and its asymptotic relative efficiency with respect to the asymptotically most powerful test against the alternative of a renewal process with gamma-distributed intervals is given.


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