Summary A test for a Poisson process based on ordered sample values is proposed and its distribution and other properties derived. The test statistic is shown to be asymptotically normal and some further approximations to its distribution are investigated. The asymptotic relative efficiency of the test with respect to the asymptotically most powerful test against the alternative of gamma-distributed intervals is derived. Finally, a test for an incomplete sample is outlined.
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Osborne Jackson (1967) studied this question.
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