BUILT-IN MATHEMATICA SYMBOL
CramerVonMisesTest
CramerVonMisesTest[data]
tests whether data is normally distributed using the Cramér-von Mises test.
CramerVonMisesTest[data, dist]
tests whether data is distributed according to dist using the Cramér-von Mises test.
- CramerVonMisesTest performs the Cramér-von Mises goodness-of-fit test with null hypothesis
that data was drawn from a population with distribution dist and alternative hypothesis 
that it was not.
- By default, a probability value or
-value is returned.
- A small
-value suggests that it is unlikely that the data came from dist.
- The dist can be any symbolic distribution with numeric and symbolic parameters or a dataset.
- The data can be univariate
or multivariate 
.
- The Cramér-von Mises test assumes that the data came from a continuous distribution.
- The Cramér-von Mises test effectively uses a test statistic based on the expectation value of
where 
is the empirical CDF of data and 
is the CDF of dist.
- For univariate data, the test statistic is given by
.
- For multivariate tests, the sum of the univariate marginal
-values is used and is assumed to follow a UniformSumDistribution under 
.
- CramerVonMisesTest[data, dist, "HypothesisTestData"] returns a HypothesisTestData object htd that can be used to extract additional test results and properties using the form htd["property"].
- CramerVonMisesTest[data, dist, "property"] can be used to directly give the value of
.
- Properties related to the reporting of test results include:
-
| "PValue" |  -value |
| "PValueTable" | formatted version of  |
| "ShortTestConclusion" | a short description of the conclusion of a test |
| "TestConclusion" | a description of the conclusion of a test |
| "TestData" | test statistic and  -value |
| "TestDataTable" | formatted version of  |
| "TestStatistic" | test statistic |
| "TestStatisticTable" | formatted  |
- The following properties are independent of which test is being performed.
- Properties related to the data distribution include:
-
| "FittedDistribution" | fitted distribution of data |
| "FittedDistributionParameters" | distribution parameters of data |
- The following options can be given:
-
- 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->"MonteCarlo",
datasets of the same length as the input 
are generated under 
using the fitted distribution. The empirical distribution from CramerVonMisesTest[si, dist, "TestStatistic"] is then used to estimate the 
-value.
Perform a Cramér-von Mises test for normality:
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Confirm the result using QuantilePlot:
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Test the fit of some data to a particular distribution:
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| Out[3]= |  |
Compare the distributions of two datasets:
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New in 8
.
-values
