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Weighted Kolmogorov-Smirnov test: Accounting for the tails


  • R'emy Chicheportiche
  • Jean-Philippe Bouchaud


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)].

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  • R'emy Chicheportiche & Jean-Philippe Bouchaud, 2012. "Weighted Kolmogorov-Smirnov test: Accounting for the tails," Papers 1207.7308,, revised Oct 2012.
  • Handle: RePEc:arx:papers:1207.7308

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    References listed on IDEAS

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    6. Griselda Deelstra & Ahmed Ezzine & Dries Heyman & Michèle Vanmaele, 2007. "Managing value-at-risk for a bond using bond put options," Computational Economics, Springer;Society for Computational Economics, vol. 29(2), pages 139-149, March.
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    Cited by:

    1. repec:wsi:ijfexx:v:02:y:2015:i:03:n:s2424786315500334 is not listed on IDEAS
    2. David M. Kaplan & Matt Goldman, 2013. "Comparing distributions by multiple testing across quantiles or CDF values," Working Papers 16-19, Department of Economics, University of Missouri, revised 22 Feb 2018.
    3. Brzezinski, Michal, 2014. "Do wealth distributions follow power laws? Evidence from ‘rich lists’," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 406(C), pages 155-162.
    4. R'emy Chicheportiche & Jean-Philippe Bouchaud, 2013. "Some applications of first-passage ideas to finance," Papers 1306.3110,
    5. David M. Kaplan & Matt Goldman, 2013. "Comparing distributions by multiple testing across quantiles," Working Papers 13-19, Department of Economics, University of Missouri, revised Feb 2018.

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