Cramer-smirnov-von-mises test

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 S_N (x) with a hypothesis function whose cumulative distribution is F(x) and whose density function is f(x), the value W² is calculated:

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

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