fix(distributions): improve lower tail numerical stability in Moyal logcdf (#8437)

[sonusharma6-dsa]

Description

In pymc.distributions.continuous.Moyal.logcdf, res was previously computed as pt.log(pt.erfc(pt.exp(-scaled / 2) * (2**-0.5))). For large negative value (scaled = (value - mu) / sigma << 0), pt.exp(-scaled / 2) grows large, causing pt.erfc(...) to underflow to 0.0 and pt.log(0.0) to return -inf.

This PR switches to pt.erfcx(u) for u > 1.0 using the identity log(erfc(u)) = log(erfcx(u)) - u**2, preventing premature numerical underflow to -inf in the lower tail while maintaining double-precision accuracy across all inputs.

Added unit test test_moyal_logcdf_lower_tail in tests/distributions/test_continuous.py.

Related Issue

• Closes BUG: Moyal logcdf returns -inf in lower tail where value is finite #8437
• Related to #

Checklist

• Checked that the pre-commit linting/style checks pass
• Included tests that prove the fix is effective or that the new feature works
• Added necessary documentation (docstrings and/or example notebooks)
• If you are a pro: each commit corresponds to a relevant logical change

Type of change

• New feature / enhancement
• Bug fix
• Documentation
• Maintenance
• Other (please specify):

[read-the-docs-community]

Documentation build overview

📚 pymc | 🛠️ Build #34557236 | 📁 Comparing a9e414d against latest (3f3b108)

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5 files changed · ± 5 modified

± Modified

• glossary.html
• _modules/pymc/backends/arviz.html
• _modules/pymc/distributions/continuous.html
• _modules/pymc/gp/hsgp_approx.html
• api/distributions/generated/pymc.Rice.html

[sonusharma6-dsa]

pre-commit.ci autofix

[drkotireddysaripalli]

The added lower-tail regression test appears to need a different reference. At a9e414d, line 963, expected comes from st.moyal.logcdf.

In SciPy 1.18.0, moyal_gen does not override _logcdf; its _cdf evaluates erfc(exp(-x/2)/sqrt(2)). The inherited rv_continuous._logcdf takes log(_cdf) below the median. That reference therefore has the same CDF-before-log underflow problem. Equal -inf values can satisfy assert_allclose (confirmed locally with NumPy 2.3.5), while a finite corrected result would disagree with that reference.

For z = (x - mu) / sigma, the CDF identity is F(x) = erfc(exp(-z/2)/sqrt(2)) = 2*Phi(-exp(-z/2)). A proposed independent reference using the normal log-CDF function is:

from scipy.special import log_ndtr

# For this test's mu=0, sigma=1 and xs=[-10, -20, -50]:
expected = np.log(2.0) + log_ndtr(-np.exp(-xs / 2.0))
assert np.isfinite(expected).all()
assert np.isfinite(res).all()
np.testing.assert_allclose(res, expected, rtol=1e-5)

I checked the pinned source paths and a standard-library erfc underflow calculation; I have not run the PyMC/SciPy test suite here. This feedback concerns the test reference for these finite lower-tail inputs, without assessing the other changes in this PR.

Prepared with Codex for a source-based numerical-methods clarification. Affiliation: Bharath Healthcare / Pinnacle Blooms Network.

[sonusharma6-dsa]

Thanks for catching this. I missed that scipy.stats.moyal.logcdf has the same underflow problem, so it isn't a reliable reference for this test.

I'll switch to the log_ndtr reference you suggested and add explicit finiteness checks for both the expected and computed values. That should make the test catch the original bug instead of passing on matching -inf values.

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