Kolmogorov-Smirnov Algorithm

Computes the difference of the distributions of two empirical observation sets.

K-S Statistic

  1. $N_1$ is the size of group 1
  2. $N_2$ is the size of group 2

  1. $S_{N_1}(x)$ is the empirical distribution of group 1
  2. $S_{N_2}(x)$ is the empirical distribution of group 2

 \begin{displaymath} D=max_{-\infty<x<\infty}|S_{N_1}(x)-S_{N_2}(x)| \end{displaymath}

K-S Significance

 \begin{displaymath} Q_{KS}(\lambda)=2\Sigma_{j=1}^\infty(-)^{j-1}e^{-2j^2\lambda^2} \end{displaymath}

Probability (D > observed) =  \begin{displaymath} Q_{KS}(\sqrt{\frac{N_1*N_2}{N_1+N_2}}*D) \end{displaymath}
Topic revision: r4 - 04 May 2009, WikiGuest
 

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