Typo in the doc of the Kstwobign distribution

[gianlucadetommaso]

Issue with current documentation:

In the documentation of the KStwobign Distribution, $D_{n,m}$ should not be square rooted when taking the limit for $n,m\to +\infty$.

Idea or request for content:

No response

Additional context (e.g. screenshots, GIFs)

Reference: https://projecteuclid.org/journals/annals-of-mathematical-statistics/volume-19/issue-2/On-the-Kolmogorov-Smirnov-Limit-Theorems-for-Empirical-Distributions/10.1214/aoms/1177730243.full, page 2.

[mdhaber]

It does look like there is a typo. Page 2 is pretty clear, but just to confirm:

import numpy as np
from scipy import stats
import matplotlib.pyplot as plt

rng = np.random.default_rng(23598345982)
m, n = 1000, 1000
N = 9999
x = rng.random((N, m))
y = rng.random((N, n))
res = stats.ks_2samp(x, y, axis=-1)
stat1 = np.sqrt((m*n)/(m + n) * res.statistic)
stat2 = np.sqrt((m*n)/(m + n)) * res.statistic

p = np.linspace(0, 10, 300)
pdf =  stats.kstwobign.pdf(p) 
bins = np.linspace(0, 10, 50)
plt.plot(p, pdf, label='pdf')
plt.hist(stat1, label='main', alpha=0.5, density=True)
plt.hist(stat2, label='suggested', alpha=0.5, density=True)
plt.legend()

@gianlucadetommaso Would you like to submit a PR? The file to edit is scipy/doc/source/tutorial/stats/continuous_kstwobign.rst. I can merge it.

[gianlucadetommaso]

Thanks for the quick reply! Sure, this should do it!