title: Weighted Kolmogorov-Smirnov test: accounting for the tails.
abstract: 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)].
authors.affiliation: Capital Fund Management, 75 007 Paris, France.
authors.forename: Rémy
authors.initials: R
authors.lastname: Chicheportiche
authors.forename: Jean-Philippe
authors.initials: JP
authors.lastname: Bouchaud
mesh_terms: D000465:Algorithms; D001703:Biophysics / Q000379:methods*; D001835:Body Weight; D005376:Financial Management; D005844:Geology; D006801:Humans; D015233:Models, Statistical; D016011:Normal Distribution; D010825:Physics / Q000379:methods; D011336:Probability; D012107:Research Design; D018709:Statistics, Nonparametric