Dept of Bioenvironmental Systems Engineering

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Goodness-of-fit TestsChi-Square GOF
testKolmogorov-Smirnov GOF test

• Professor Ke-Sheng Cheng
• Department of Bioenvironmental Systems
  Engineering
• National Taiwan University

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Chi-square GOF test Concept
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Chi-square GOF test
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Kolmogorov-Smirnov GOF testConcept
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Kolmogorov-Smirnov GOF test

• The chi-square test compares the empirical
  histogram against the theoretical histogram.
• In contrast, the K-S test compares the empirical
  cumulative distribution function (ECDF) against
  the theoretical CDF.

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• In order to measure the difference between Fn(X)
  and F(X), ECDF statistics based on the vertical
  distances between Fn(X) and F(X) have been
  proposed.

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Values of for the Kolmogorov-Smirnov test