Cramer-von-Mises criterion

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In statistics the Cramer-von-Mises criterion for judging the goodness of fit of a probability distribution F * (x) compared to a given distribution F is given by

W^2 = \int_{-\infty}^\infty [F(x)-F^*(x)]^2 dF(x)

In applications F(x) is the theoretical distribution and F * is the empirically observed distribution.

The Cramer-von-Mises test is an alternative to the Kolmogorov-Smirnov test.

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