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Kolmogorov Test

  A powerful test (also called Kolmogorov-Smirnov test) that a one-dimensional data sample is compatible with being a random sampling from a given distribution. It is also used to test whether two data samples are compatible with being random samplings of the same, unknown distribution. It is similar to the Cramer-Smirnov-Von-Mises test, but somewhat simpler.

To compare a data sample consisting of N events whose cumulative distribution is SN(x) with a hypothesis function whose cumulative distribution is F(x), the value DN is calculated:

The confidence levels for some values of are (for N > 80):


To compare two experimental cumulative distributions SN(x) containing N events, and SM(x) containing M events, calculate:

Then is the test statistic for which the confidence levels are as in the above table. For more detail, [Press95].

Rudolf K. Bock, 7 April 1998