View source for Cramer-smirnov-von-mises test



A powerful test that a one-dimensional data sample is compatible with being a random sampling from a given distribution. It is also used to test whether two data samples are compatible with being random samplings of the same, unknown distribution. It is similar to the [[Kolmogorov test#142|Kolmogorov test]], but somewhat more complex computationally.

To compare data consisting of ''N'' events whose cumulative distribution is ''S''<sub>''N''</sub> (''x'') with a hypothesis function whose cumulative distribution is ''F''(''x'') and whose density function is ''f''(''x''), the value ''W''<sup>2</sup> is calculated:

[[File:hepa_img222.gif|374x38px]]

The confidence levels for some values of ''NW''<sup>2</sup> are ( [[File:hepa_img1.gif|14x8px]] [[References 1#eadi71|Eadie71]]) for ''N''&gt;3:

<div align="CENTER">

conf.l.
''NW''<sup>2</sup>
10%
0.347
5%
0.461
1%
0.743

</div>

[[Category:W.Krisher and R.Bock]]
[[Category:Data analysis]]
[[Category:Statistics]]

{{Sourceattribution|Cramer-smirnov-von-mises test|1}}