Cramér-von-Mises criterion
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In statistics the Cramér-von-Mises criterion for judging the goodness of fit of a probability distribution F * compared to a given distribution F is given by
![W^2 = \int_{-\infty}^\infty [F(x)-F^*(x)]^2 dF(x)](../../../math/4/4/2/442818e665f107c389dcb4591b9b971e.png)
In applications F is the theoretical distribution and F * is the empirically observed distribution.
The criterion is named after Harald Cramér and Richard Edler von Mises.
The Cramér-von-Mises test is an alternative to the Kolmogorov-Smirnov test.
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