Lesson 22: Kolmogorov-Smirnov Goodness-of-Fit Test

Overview Section

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In this lesson, we'll learn how to conduct a test to see how well a hypothesized distribution function \(F(x)\) fits an empirical distribution function \(F_{n}(x)\). The "goodness-of-fit test" that we'll learn about was developed by two probabilists, Andrey Kolmogorov and Vladimir Smirnov, and hence the name of this lesson. In the process of learning about the test, we'll:

  • learn a formal definition of an empirical distribution function
  • justify, but not derive, the Kolmogorov-Smirnov test statistic
  • try out the test on a few examples
  • learn how to calculate a confidence band for a distribution function \(F(x)\)