20.5.5  Testing a distribution with the Kolmogorov-Smirnov distribution

The kolmogorovt command uses the Kolmogorov test to compare sample data to a specified continuous distribution.

• kolmogorovt takes two arguments and possibly additional parameters.
  • L, a list of sample data.
  • Optionally, distr. This can be one of:
    • The name of a distribution and the necessary parameters (see Section 20.3.4 for a list of distributions and their parameters).
    • Another list of sample data.
• kolmogorovt(L,distr) returns a list of three values:
  • The D statistic, which is the maximum distance between the cumulative distribution functions of the samples or the sample and the given distribution.
  • The K value, where K=D√n (for a single data set, where n is the size of the data set) or K=D√n₁ n₂ /(n₁ + n₂) (when there are two data sets, with sizes n₁ and n₂). The K value will tend towards the Kolmogorov-Smirnov distribution as the data size approaches infinity.
  • 1-kolmogorovd(K), which will be close to 1 when the distributions look like they match.

Examples