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What is Kolmogorov–Smirnov statistic?

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The Kolmogorov-Smirnov test is a non-parametric approach for comparing an empirical CDF derived from observed data with that of a known distribution by computing the greatest distance between the two. A common application of the test is to verify the normality assumption, as in that case,  it compares the observed distribution to the quantiles of the theoretical normal distribution. However, it is very easy to reject the null hypothesis, or conclude the distributions are different, when the sample size is large, and thus it is often not as useful as residual plots and other more qualitative diagnostics produced after a model is fit

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