`geometric()` returns failures before the first success (k >= 0) instead of trials (k >= 1)

[vchamarthi]

Affects: mkl_random.MKLRandomState.geometric, mkl_random.interfaces.numpy_random.geometric, and numpy.random.geometric after mkl_random.patch_numpy_random()

Issue

Every sample from geometric(p) is one less than it should be.

NumPy defines the geometric distribution on k = 1, 2, ... with f(k) = (1 - p)^(k-1) p. mkl_random's docstring (mklrand.pyx:6018-6024) states the same, and the NumPy interface refers users to numpy.random.geometric.

irk_geometric_vec (src/mkl_distributions.cpp:1302) returns the output of viRngGeometric unchanged. oneMKL defines that output as the number of failures before the first success: P(X = k) = p (1 - p)^k for k in {0, 1, 2, ...}. The p == 1.0 branch writes 0 where NumPy returns 1.

test_randomdsit_geometric (tests/test_random.py:864) has 0 in its expected values, so the suite passes with this behaviour.

import numpy as np
import mkl_random

x = mkl_random.interfaces.numpy_random.RandomState(1).geometric(0.3, size=10**7)
print(x.min(), x.mean())                                             # 0 2.3330
print(np.random.RandomState(1).geometric(0.3, size=10**7).mean())   # 3.3331

mkl_random.patch_numpy_random()
print(np.random.geometric(0.3, size=10**6).min())                    # 0

print(mkl_random.interfaces.numpy_random.RandomState(0).geometric(1.0, 3))  # [0 0 0]; NumPy: [1 1 1]

How found

Chi-square goodness-of-fit against the exact k >= 1 pmf, with 10^7 draws and seeds 1, 2 and 3. As a control, an exact inverse-CDF sampler under the same test gives z ~ N(0, 1).

p	exact mean	mkl_random mean	mkl_random z	mkl_random + 1, z	NumPy Generator z
0.01	100.000	98.975	20.7, 20.9, 23.1	-1.4, -1.3, 0.8	-0.4, -0.7, 0.5
0.3	3.3333	2.3325	~1.0e5	-0.9, 0.3, 0.6	-1.7, -0.3, -0.4
0.5	2.0000	0.9995	~4.0e5	-1.0, 0.4, -1.7	0.7, -0.5, -0.5
0.9	1.1111	0.1109	~2.3e6	0.3, 0.3, -0.2	2.2, 1.3, 0.2

The unshifted output fits the k >= 0 pmf (z between -1.4 and 0.3). The output is bit-identical to calling viRngGeometric directly. It is also identical with oneMKL 2023.2, 2024.2.2, 2025.0.1, 2025.3.1, 2026.0 and 2026.1, and on all six BRNGs (MT19937, SFMT19937, MT2203, MCG59, PHILOX4X32X10, ARS5).

Environment: mkl_random 1.5.0 (py313h581662c_0, Intel channel), oneMKL 2026.1.0, NumPy 2.4.3, Linux x86-64.

Impact

With the patch enabled, code calling numpy.random.geometric gets different results: the mean is 1 lower, and 0 appears with probability p although NumPy never returns it. Scalar p, array p and p = 1 are all affected.

Possible fix

• Add 1 to each element after viRngGeometric in irk_geometric_vec, and write 1 in the p == 1.0 branch.
• Update the expected values in test_randomdsit_geometric. Add a test that geometric(p).min() >= 1 and that the mean is within tolerance of 1/p.
• Check the other discrete wrappers for the same oneMKL-vs-NumPy support mismatch.