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fix: stabilize Gamma PDF for finite in-range parameters #442

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fix: stabilize Gamma PDF for finite in-range parameters #442

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26 changes: 21 additions & 5 deletions src/distribution/gamma.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -361,13 +361,10 @@ impl Continuous<f64, f64> for Gamma {
0.0
} else if self.shape == 1.0 {
self.rate * (-self.rate * x).exp()
} else if self.shape > 160.0 {
self.ln_pdf(x).exp()
} else if x.is_infinite() {
0.0
} else {
self.rate.powf(self.shape) * x.powf(self.shape - 1.0) * (-self.rate * x).exp()
/ gamma::gamma(self.shape)
self.ln_pdf(x).exp()
}
}

Expand All @@ -392,10 +389,23 @@ impl Continuous<f64, f64> for Gamma {
f64::NEG_INFINITY
} else if self.shape == 1.0 {
self.rate.ln() - self.rate * x
} else if x == 0.0 {
if self.shape < 1.0 {
f64::INFINITY
} else {
f64::NEG_INFINITY
}
} else if x.is_infinite() {
f64::NEG_INFINITY
} else {
self.shape * self.rate.ln() + (self.shape - 1.0) * x.ln()
let ln_rate = self.rate.ln();
let ln_x = x.ln();
let ln_product = ln_rate + ln_x;
let virtual_ln_x = ln_product - ln_rate;
let ln_product_error = (ln_rate - (ln_product - virtual_ln_x)) + (ln_x - virtual_ln_x);
self.shape
.mul_add(ln_product, self.shape * ln_product_error)
- ln_x
- self.rate * x
- gamma::ln_gamma(self.shape)
}
Expand Down Expand Up @@ -610,6 +620,12 @@ mod tests {
// (10.0, f64::INFINITY, f64::INFINITY, 0.0, pdf(f64::INFINITY)),];
}

#[test]
fn test_pdf_with_underflowing_rate_power() {
let expected = 4.455666577035095e-7;
test_absolute(80.0, 1e-5, expected, expected * 2e-13, |dist| dist.pdf(8e6));
}

#[test]
fn test_pdf_at_zero() {
test_relative(1.0, 0.1, 0.1, |x| x.pdf(0.0));
Expand Down