MAINT: stats.monte_carlo_test: used biased estimate of p-value

[mdhaber]

Reference issue

gh-16459

What does this implement/fix?

The unbiased estimate of the p-value used in monte_carlo_test does not control the Type I error rate. This implements a biased estimate that does per [1].

import numpy as np
from scipy import stats
rng = np.random.default_rng(2190176673029737545)
x = np.zeros(100)
res = stats.monte_carlo_test(x, rng.random, np.mean,
                             vectorized=True, alternative='less')
assert res.pvalue == 0.0001

Additional information

[tupui]

Indeed, thanks Matt. It would be good to get this for the release. I tested this locally and it works as expected.