1.3.5.16. Kolmogorov-Smirnov Goodness-of-Fit Test

The Kolmogorov-Smirnov test (Chakravart, Laha, and Roy, 1967) is used to decide if a sample comes from a population with a specific distribution. The Kolmogorov-Smirnov (K-S) test is based on the empirical distribution function (ECDF). Given N ordered data points Y1, Y2, ..., YN, the ECDF is defined as \[ E_{N} = n(i)/N \] where n(i) is the number of points less than Yi and the Yi are ordered from

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K-S検定の丁寧な説明。二つの確率分布の最大距離を統計量Dとして得る。p値が低いほど二つの分布は異なっている。