Ratchet Scan and Disjoint Statistics
Joachim Krauth · Birkhäuser Boston eBooks · 1999
A general definition of ratchet scan and disjoint statistics is given. The known results for the disjoint statistic, the linear ratchet scan statistic, and the circular ratchet scan statistic are reviewed. This concerns the exact and asymptotic distributions as well as exact bounds for the upper tail probabilities of the test statistics under the null hypothesis of no clustering. Further, results concerning the power of the tests in comparison with other tests for clustering are reported. In addition, certain modifications and extensions, e.g., the EMM procedure, the Grimson models, and the test of Hewitt et al. (1971) are studied. Finally, a general approach to derive exact upper and lower bounds for the tail probabilities of the general ratchet scan statistic is described.