al
    The method used to compute the p-value, see Notes for details.
    The default is 'auto'.

Returns
-------
res : object with attributes
    statistic : float
        Cramér-von Mises statistic.
    pvalue : float
        The p-value.

See Also
--------
cramervonmises, anderson_ksamp, epps_singleton_2samp, ks_2samp

Notes
-----
.. versionadded:: 1.7.0

The statistic is computed according to equation 9 in [2]_. The
calculation of the p-value depends on the keyword `method`:

- ``asymptotic``: The p-value is approximated by using the limiting
  distribution of the test statistic.
- ``exact``: The exact p-value is computed by enumerating all
  possible combinations of the test statistic, see [2]_.

If ``method='auto'``, the exact approach is used
if both samples contain equal to or less than 20 observations,
otherwise the asymptotic distribution is used.

If the underlying distribution is not continuous, the p-value is likely to
be conservative (Section 6.2 in [3]_). When ranking the data to compute
the test statistic, midranks are used if there are ties.

References
----------
.. [1] https://en.wikipedia.org/wiki/Cramer-von_Mises_criterion
.. [2] Anderson, T.W. (1962). On the distribution of the two-sample
       Cramer-von-Mises criterion. The Annals of Mathematical
       Statistics, pp. 1148-1159.
.. [3] Conover, W.J., Practical Nonparametric Statistics, 1971.

Examples
--------

Suppose we wish to test whether two samples generated by
``scipy.stats.norm.rvs`` have the same distribution. We choose a
significance level of alpha=0.05.

>>> import numpy as np
>>> from scipy import stats
>>> rng = np.random.default_rng()
>>> x = stats.norm.rvs(size=100, random_state=rng)
>>> y = stats.norm.rvs(size=70, random_state=rng)
>>> res = stats.cramervonmises_2samp(x, y)
>>> res.statistic, res.pvalue
(0.29376470588235293, 0.1412873014573014)

The p-value exceeds our chosen significance level, so we do not
reject the null hypothesis that the observed samples are drawn from the
same distribution.

For small sample sizes, one can compute the exact p-values:

>>> x = stats.norm.rvs(size=7, random_state=rng)
>>> y = stats.t.rvs(df=2, size=6, random_state=rng)
>>> res = stats.cramervonmises_2samp(x, y, method='exact')
>>> res.statistic, res.pvalue
(0.197802197802198, 0.31643356643356646)

The p-value based on the asymptotic distribution is a good approximation
even though the sample size is small.

>>> res = stats.cramervonmises_2samp(x, y, method='asymptotic')
>>> res.statistic, res.pvalue
(0.197802197802198, 0.2966041181527128)

Independent of the method, one would not reject the null hypothesis at the
chosen significance level in this example.

r