Fix the second-order moment equations to match Cox (1979) - #52
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rawmoment() diverged from the equations in the Appendix of N. D. Cox,
"Tolerance Analysis by Computer", Journal of Quality Technology 11(2),
1979. The mean and variance (A-6, A-7) were correct, but the third raw
moment was wrong for n >= 3 inputs and the fourth for n >= 2.
Nine defects, each checked against the printed equations on pp. 86-87 and
against two independent oracles (exact polynomial expansion of E[y^k],
and tensor-product Gauss-Hermite/Gauss-Laguerre quadrature):
1. (A-8) triple sum used vm[m,1] instead of vm[m,2]. The first
standardized moment is zero, so this silently dropped the term.
2. (A-9) pair term used mu_j6 instead of mu_j5 in
12 b_ij b_ii b_jj [b_ii mu_i5 mu_j3 + b_jj mu_i3 mu_j5].
3-5. (A-9) three terms indexed mu_i2 where the paper has mu_j2.
6. (A-9) triple sum used 6 b_ii^2 b_jk instead of 6 b_ii^2 b_jk^2.
7. (A-9) triple sum used 24 b_ii b_kk b_ik b_jk instead of
24 b_ii b_jj b_ik b_jk.
8. (A-9) emitted two mu_i2 mu_j3 mu_k3 blocks, double counting three
terms; the paper has one.
9. (A-9) quadruple sum used b_jj b_ik b_im b_im instead of
b_jj b_ik b_im b_km.
With these corrected, Cox's Table 2 reproduces: mean 1176.45, variance
99,699.68, and skewness 0.7100769 against the paper's 0.7100789 (it was
0.7080131). Table 2's printed kurtosis of 6.183188 is not reproducible
from equation (A-9) itself, which gives 6.161161; the code follows the
equation, and test_assembly.py records why.
Also fixed, found while verifying the surrounding layers:
- umath.cot() computed tan() where it needed csc(), so both the first and
second derivatives were wrong.
- UncertainVariable(rv=...) ignored loc/scale and skipped standardization
for distributions with no shape parameter, so U(a, b) returned
unstandardized moments (mu_4 = 0.0125 rather than 1.8). Both branches
now integrate the standardized central moments directly, which also
avoids the cancellation the raw-moment route suffers when the mean is
large relative to the spread.
docs/theory.md carried five equation errors of its own, independent of
the code; these are corrected, and the blocks previously elided as
"similar terms" are written out in full. Stale published results in
README.md, soerp_examples.py and the uv docstring are updated.
Co-authored-by: codex <267193182+codex@users.noreply.github.com>
Co-authored-by: Claude Opus 5 <noreply@anthropic.com>
Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
Codecov Report✅ All modified and coverable lines are covered by tests. 📢 Thoughts on this report? Let us know! |
soerp_examples.py printed the same four "Results should be about" literals for each of the three ways every example is built, which SonarQube flagged as duplicated string literals on new code. The reference values now live in one tuple per example alongside a print_expected() helper. The script's output is byte-for-byte unchanged. The previous commit also left four lines uncovered: - umath.cot() had no test at all, so its corrected derivatives went unverified by CI. TestCot pins cot' = -csc**2 and cot'' = 2*cot*csc**2, which is precisely what the earlier tan()-based version got wrong. It sits in its own class to stay under the per-class public-method limit. - The two shape-parameter guards in UncertainVariable.__init__ were never exercised. scipy validates shape arguments when a distribution is frozen, so an inconsistent rv cannot be constructed directly; the tests set `args` on the frozen object to reach soerp's own guard, which is also what protects duck-typed, non-scipy rv objects. tests/test_uncertain_variable.py additionally locks down the standardization fix from the previous commit: moments 3-8 must depend only on distribution shape, so U(2, 6) now yields mu_4 = 1.8 and the normal moments are invariant to loc and scale. Co-authored-by: gemini-code-assist <gemini-code-assist@users.noreply.github.com> Co-authored-by: Junie <junie@jetbrains.com> Co-authored-by: Qwen-Coder <qwen-coder@alibabacloud.com> Co-authored-by: Cursor Agent <cursoragent@cursor.com> Co-authored-by: kilocode-bot <github-actions@github.com>
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rawmoment() diverged from the equations in the Appendix of N. D. Cox, "Tolerance Analysis by Computer", Journal of Quality Technology 11(2),
1979. The mean and variance (A-6, A-7) were correct, but the third raw moment was wrong for n >= 3 inputs and the fourth for n >= 2.
Nine defects, each checked against the printed equations on pp. 86-87 and against two independent oracles (exact polynomial expansion of E[y^k], and tensor-product Gauss-Hermite/Gauss-Laguerre quadrature):
With these corrected, Cox's Table 2 reproduces: mean 1176.45, variance 99,699.68, and skewness 0.7100769 against the paper's 0.7100789 (it was 0.7080131). Table 2's printed kurtosis of 6.183188 is not reproducible from equation (A-9) itself, which gives 6.161161; the code follows the equation, and test_assembly.py records why.
Also fixed, found while verifying the surrounding layers:
docs/theory.md carried five equation errors of its own, independent of the code; these are corrected, and the blocks previously elided as "similar terms" are written out in full. Stale published results in README.md, soerp_examples.py and the uv docstring are updated.