BUG: scipy.stats.multivariate_hypergeom.rvs raises ValueError when at least the last two populations are 0

Describe your issue.

I ran into a strange issue when sampling using Scipy’s multivariate hypergeometric distribution. Calling scipy.stats.multivariate_hypergeom.rvs on a list of populations raises the error message ValueError: ngood + nbad < nsample, while calling the same function on the sorted array as input does not. Specfically, the error seems to be raised when at least the last two values of the population are 0.

Reproducing Code Example

import scipy.stats
r = scipy.stats.multivariate_hypergeom.rvs
res1 = r([0, 20], 5) # Returns [0, 5]
res2 = r([0, 0, 20], 5) # Returns [0, 0, 5]
res3 = r([0, 0, 20, 0], 5) # # Returns [0, 0, 5, 0]
res4 = r([0, 0, 20, 0, 0], 5) # # Raises error

Error message

Traceback (most recent call last):
  File "<string>", line 6, in <module>
  File "/home/alexander/miniconda3/envs/py37/lib/python3.7/site-packages/scipy/stats/_multivariate.py", line 4726, in rvs
    size=size))
  File "mtrand.pyx", line 3839, in numpy.random.mtrand.RandomState.hypergeometric
ValueError: ngood + nbad < nsample

SciPy/NumPy/Python version information

1.7.3 1.21.5 sys.version_info(major=3, minor=10, micro=4, releaselevel=‘final’, serial=0)

[WarrenWeckesser]

My comment about the arguments being invalid needs some qualification.

If we could rely on random_state being a Generator instance (i.e. if we could ensure that we were using the new NumPy random API instead of the legacy API), we could replace that line with:

            rvs[..., c] = random_state.hypergeometric(m[..., c], rem, n,
                                                      size=size)

n might be 0, but Generator.hypergeometric will do the right thing. For example,

In [8]: rng = np.random.default_rng()

In [9]: rng.hypergeometric(0, 1, 0)
Out[9]: 0

In [10]: rng.hypergeometric(1, 0, 0)
Out[10]: 0

In [11]: rng.hypergeometric(0, 0, 0)
Out[11]: 0

The reason for the shenanigans with n != 0 and n == 0 is that we have to support the legacy random API (and we have to support broadcasting, so we can’t use a simple if statement), and np.random.hypergeometric doesn’t allow n == 0:

In [16]: np.random.hypergeometric(0, 1, 0)
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [16], in <module>
----> 1 np.random.hypergeometric(0, 1, 0)

File mtrand.pyx:3871, in numpy.random.mtrand.RandomState.hypergeometric()

File _common.pyx:919, in numpy.random._common.disc()

File _common.pyx:436, in numpy.random._common.check_constraint()

ValueError: nsample < 1 or nsample is NaN

The code as written fixes that problem by multiplying the result of random_state.hypergeometric() by (n != 0); this ensures that wherever n is 0, the result is 0. It passes the argument n + (n == 0) to random_state.hypergeometric() to prevent the ValueError from being raised in that case. However, we missed the case where both of the first two arguments to hypergeometric() are 0. In that case, our code does, in effect:

In [18]: np.random.hypergeometric(0, 0, 1)
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [18], in <module>
----> 1 np.random.hypergeometric(0, 0, 1)

File mtrand.pyx:3870, in numpy.random.mtrand.RandomState.hypergeometric()

ValueError: ngood + nbad < nsample

One way to fix this is to add (n == 0) to rem in addition to n:

            n0mask = n == 0
            rvs[..., c] = (~n0mask *
                           random_state.hypergeometric(m[..., c],
                                                       rem + n0mask,
                                                       n + n0mask,
                                                       size=size))

[WarrenWeckesser]

@tirthasheshpatel, I probably wouldn’t get to a PR right away, so if you have time now, go for it!