Chicheportiche Rémy, Bouchaud Jean-Philippe
Capital Fund Management, 75 007 Paris, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Oct;86(4 Pt 1):041115. doi: 10.1103/PhysRevE.86.041115. Epub 2012 Oct 10.
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)].
对经验分布的极端尾部进行精确的拟合优度检验是一个非常重要的问题，在许多领域都有相关性，包括地球物理学、保险和金融。我们已经推导出了适用于检验这些极端尾部的大样本柯尔莫哥洛夫-斯米尔诺夫检验的一种推广形式的精确渐近结果。顺便提一下，我们重新推导并更精确地给出了最初在不相关领域中找到的近似极限解，最早在[L. 图尔班，《物理学报A》25, 127 (1992)]中，后来在[P. L. 克拉皮夫斯基和S. 雷德纳，《美国物理杂志》64, 546 (1996)]中。
