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Accurate goodness-of-fit tests for the extreme tails of empirical distributions is a very important issue, relevant in many contexts, including geophysics, insurance, and finance. We have derived exact asymptotic results for a generalization of the large-sample Kolmogorov-Smirnov test, well suited to testing these extreme tails. In passing, we have rederived and made more precise the approximate limit solutions found originally in unrelated fields, first in [L. Turban, J. Phys. A 25, 127 (1992)] and later in [P. L. Krapivsky and S. Redner, Am. J. Phys. 64, 546 (1996)].


Rémy Chicheportiche, Jean-Philippe Bouchaud. Weighted Kolmogorov-Smirnov test: accounting for the tails. Physical review. E, Statistical, nonlinear, and soft matter physics. 2012 Oct;86(4 Pt 1):041115

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PMID: 23214537

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