For a test for goodness of fit, a cutoff is chosen such that is rejected only if . The value of used for the and properties is controlled by the SignificanceLevel option. By default is set to .
With the setting Method, datasets of the same length as the input are generated under using the fitted distribution. The empirical distribution from CramerVonMisesTest is then used to estimate the -value.
Estimate the power of the Cramér-von Mises test when the underlying distribution is UniformDistribution, the test size is , and the sample size is 32:
Observations generated by a homogeneous Poisson process should exhibit complete spatial randomness, which implies that they were drawn from a uniform distribution. Determine if observations from the following images would be modeled well by a homogeneous Poisson process:
Find the centers of each point and rescale on :
The points in the first image would be modeled well by a homogeneous Poisson process:
A model for the second group should account for dependence:
Find the parameters for distributions that minimize the Cramér-von Mises test statistic: