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The signed rank test currently is only an approximation for large values (see #182 (comment))
There is a valid wilcoxon distribution that is quite expensive to calculate. Nevertheless it is required to calculate exact u test results, and should be implemented:
The "Wilcoxon distribution" referenced here is the exact null distribution of the Wilcoxon rank-sum statistic (used for the two-sample Mann-Whitney U test), distinct from the approximate normal distribution the signed-rank test currently uses.
What's needed:
A DP-based CDF for the Wilcoxon rank-sum distribution: count the number of m-subsets of {1,...,m+n} that sum to ≤ w (the R wilcox.c algorithm). This is O(m·n·m·n) in the worst case but very fast for small samples.
An exact variant of MannWhitneyUTest.computeUtest that uses the exact CDF for small samples (say m·n ≤ 400) and falls back to the normal approximation otherwise.
PR FR: Mann-Whitney-U test #182 (omaus/FSharp.Stats) added a UTest.fs with a normal-approximation U-test but has had merge conflicts since 2022 — the implementation logic is sound and could be the starting point.
I'll look at implementing this in a future run, as I already have an open PR batch for this cycle.
Activity
removed obsolete wilcoxon distribution fslaborg#213
bvenn commentedon Jun 28, 2022
The signed rank test currently is only an approximation for large values (see #182 (comment))
There is a valid wilcoxon distribution that is quite expensive to calculate. Nevertheless it is required to calculate exact u test results, and should be implemented:
References:
[-]obsolete Wilcoxon Distribution [/-][+]Add Wilcoxon Distribution [/+]github-actions commentedon Apr 12, 2026
🤖 This is an automated response from Repo Assist.
The "Wilcoxon distribution" referenced here is the exact null distribution of the Wilcoxon rank-sum statistic (used for the two-sample Mann-Whitney U test), distinct from the approximate normal distribution the signed-rank test currently uses.
What's needed:
{1,...,m+n}that sum to ≤ w (the Rwilcox.calgorithm). This is O(m·n·m·n) in the worst case but very fast for small samples.MannWhitneyUTest.computeUtestthat uses the exact CDF for small samples (say m·n ≤ 400) and falls back to the normal approximation otherwise.omaus/FSharp.Stats) added aUTest.fswith a normal-approximation U-test but has had merge conflicts since 2022 — the implementation logic is sound and could be the starting point.I'll look at implementing this in a future run, as I already have an open PR batch for this cycle.