Cramer-smirnov-von-mises test

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A powerful 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 Kolmogorov test, but somewhat more complex computationally.

To compare data consisting of N events whose cumulative distribution is SN (x) with a hypothesis function whose cumulative distribution is F(x) and whose density function is f(x), the value W2 is calculated:

Hepa img222.gif

The confidence levels for some values of NW2 are ( Hepa img1.gif Eadie71) for N>3:

conf.l. NW2 10% 0.347 5% 0.461 1% 0.743