fix: stabilize Gamma PDF for finite in-range parameters - #442
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Codecov Report✅ All modified and coverable lines are covered by tests. Additional details and impacted files@@ Coverage Diff @@
## main #442 +/- ##
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+ Coverage 95.42% 95.45% +0.02%
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Files 65 65
Lines 15204 15281 +77
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+ Hits 14509 14586 +77
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Included review availability: Your plan provides up to 10 included reviews per hour; 8 remain after this review. 📝 WalkthroughWalkthroughThe Gamma distribution now derives non-unit-shape PDF values from ChangesGamma PDF stability
Estimated code review effort: 3 (Moderate) | ~20 minutes Merge Risk: 🟡 Moderate · up to The Gamma PDF update improves stability for finite in-range inputs but leaves an edge-case contract mismatch at x = 0 when parameters are individually infinite: it can return finite or infinite values where the documented result is NaN. This bounded correctness risk requires explicit owner acceptance or follow-up before merge. 🚥 Pre-merge checks | ✅ 5✅ Passed checks (5 passed)
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Inline comments:
In `@src/distribution/gamma.rs`:
- Around line 392-397: The x == 0.0 branch in the Gamma density methods must
return f64::NAN when either accepted parameter is infinite, before applying the
shape-based ±infinity logic. Update the relevant Gamma implementation and add
coverage for pdf(0.0) and ln_pdf(0.0) with infinite shape and infinite rate.
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Correctness
Performance (
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| shape | rate | R | SciPy | mpmath (50 dps) | statrs upstream (pre-PR) | statrs PR #442 (before fix) | statrs PR #442 (after fix) |
|---|---|---|---|---|---|---|---|
| ∞ | 1.0 | 0.73 µs | 67.7 µs | 11.1 µs | 2.0 ns | 3.3 ns | 2.7 ns |
| 0.5 | ∞ | 11.9 µs | 36.7 µs | 7.6 µs | 9.9 ns | 6.1 ns | 3.7 ns |
| 2.0 | ∞ | 11.7 µs | 36.8 µs | 16.8 µs | 19.0 ns | 4.3 ns | 3.7 ns |
| 1.0 | ∞ | 11.9 µs | 36.6 µs | 16.9 µs | 3.7 ns | 4.4 ns | 3.7 ns |
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Inline comments:
In `@src/distribution/gamma.rs`:
- Around line 403-406: In the Gamma log-density path containing the frexp
calculations, add an infinite-rate guard immediately after the existing
x.is_infinite() branch so self.rate == f64::INFINITY returns NaN before frexp is
called. Add a regression test using x = 1.0 that verifies the infinite-rate case
produces NaN.
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well this does now fail a doctest at 1e-15 absolute error... |
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You're right — decomposing the product is the better approach here because it preserves the dynamic range without relying on compensated |
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Summary
ln_pdf().exp()to avoid overflow/underflow in separately evaluated factorsx = 0,x = +inf, andshape = 1ln(rate) + ln(x)before multiplying byshapeGamma(80, 1e-5).pdf(8e6)Root cause
The previous formula evaluated
rate.powf(shape)independently. For valid finite parameters this factor could underflow to zero while the remaining factors compensated it mathematically, producingNaNinstead of a finite density.TDD and independent numerical references
The regression case is
Gamma(shape=80, rate=1e-5).pdf(8e6).4.455666577034977970e-72.63e-144.455666577035076430e-74.22e-15dgamma4.455666577035096020e-71.81e-164.45566657703509521452812298721e-74.455666577035271250e-73.95e-14Upstream statrs returns
NaN; the regression test is red on upstream and green with this change. R and Boost.Math are more accurate for this input; this change is more accurate than SciPy.Performance
Gamma(80, 1e-5).pdf(8e6)NaNstdfeatures-O3 -march=nativedgammagamma.pdfRelated issue
Fixes #422 —
Gamma::pdfreturnsNaNfor ordinary, finite, in-range parameters.Summary by CodeRabbit