Cramer-von-Mises criterion

In statistics the Cramér–von Mises criterion is a criterion used for judging the goodness of fit of a cumulative distribution function ${\displaystyle F^{*}}$ compared to a given empirical distribution function ${\displaystyle F_{n}}$, or for comparing two empirical distributions. It is also used as a part of other algorithms, such as minimum distance estimation. It is defined as

In one-sample applications ${\displaystyle F^{*}}$ is the theoretical distribution and ${\displaystyle F_{n}}$ is the empirically observed distribution. Alternatively the two distributions can both be empirically estimated ones; this is called the two-sample case.

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