Cramér–von Mises criterion
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In statistics the Cramér–von Mises criterion is a criterion used for judging the goodness of fit of a cumulative distribution function compared to a given empirical distribution function , 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
This article may be too technical for most readers to understand. (July 2023) |
In one-sample applications is the theoretical distribution and is the empirically observed distribution. Alternatively the two distributions can both be empirically estimated ones; this is called the two-sample case.
The criterion is named after Harald Cramér and Richard Edler von Mises who first proposed it in 1928–1930.[1][2] The generalization to two samples is due to Anderson.[3]
The Cramér–von Mises test is an alternative to the Kolmogorov–Smirnov test (1933).[4]