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BUG: fix negative samples generated by Wald distribution #29609

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BUG: fix negative samples generated by Wald distribution #29609

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1032796
BUG: improved numerical stability of Wald sample generation
mmaaz-git Aug 21, 2025
7e7e281
Removed mu_2l variable
mmaaz-git Aug 21, 2025
ff74d8d
changed test case
mmaaz-git Aug 21, 2025
d54d7f4
check for 0 normal rv and simplify expressions
mmaaz-git Aug 24, 2025
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9 changes: 6 additions & 3 deletions numpy/random/src/distributions/distributions.c
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Original file line number Diff line number Diff line change
Expand Up @@ -845,12 +845,15 @@ double random_noncentral_f(bitgen_t *bitgen_state, double dfnum, double dfden,

double random_wald(bitgen_t *bitgen_state, double mean, double scale) {
double U, X, Y;
double mu_2l;
double d;

mu_2l = mean / (2 * scale);
Y = random_standard_normal(bitgen_state);
if (Y == 0) {
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does the Y need to be exactly 0 or close to zero within some epsilon like fabs(Y) < 1e-12 ?

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That's a good question. I tried it with forcing Y=1e-10 or 1e-15, etc, and it doesn't seem to cause any issues.

For what it's worth, I realized that even without the check for if (Y==0), it's still fine when Y=0, because you get d=inf (per the IEEE standard), and then X = mean * (1 - d/inf) = mean.

I'm not sure what is the usual numpy practice here -- can we rely on inf as an intermediate step?

return mean;
}
Y = mean * Y * Y;
X = mean + mu_2l * (Y - sqrt(4 * scale * Y + Y * Y));
d = 1 + sqrt(1 + 4 * scale / Y);
X = mean * (1 - 2 / d);
U = next_double(bitgen_state);
if (U <= mean / (mean + X)) {
return X;
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5 changes: 5 additions & 0 deletions numpy/random/tests/test_generator_mt19937.py
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Expand Up @@ -1874,6 +1874,11 @@ def test_wald(self):
[2.07093587449261, 0.73073890064369]])
assert_array_almost_equal(actual, desired, decimal=14)

def test_wald_nonnegative(self):
random = Generator(MT19937(self.seed))
samples = random.wald(mean=1e9, scale=2.25, size=1000)
assert_(np.all(samples >= 0.0))

def test_weibull(self):
random = Generator(MT19937(self.seed))
actual = random.weibull(a=1.23, size=(3, 2))
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