Beta random number generator can produce values outside its domain

The numpy.random.beta function can generate samples that are either 0 or 1, which is outside of the support of the Beta distribution.

We came across this issue over at pymc3. I started to dig into it and found that numpy’s legacy implementation can in fact produce zeros and ones if the a and b parameters are both smaller than 1.

I read a bit of Johnk’s method here, and it seems acceptable to discard the generated sample if it is either 0 or 1. That way, you would always end with generated random number in the open (0, 1) domain.

Reproducing code example:

>>> import numpy as np
>>> a = np.random.beta(0.01, 0.01, size=1000000)
>>> print(np.any(a == 0), np.any(a == 1))
True, True

Numpy/Python version information:

1.18.1 3.7.6 (default, Jan 8 2020, 19:59:22) [GCC 7.3.0]

[WarrenWeckesser]

There are a lot more exact 1s than exact 0s, but with a==b, the two ends ought to be symmetric.

Could that be because there are more floating point numbers near 0 than there are near 1?

[lucianopaz]

@VikrantReddy, that’s what the PR I opened, #16231 did, it discarded the samples that were equal to zero or one, and resampled them. Unfortunately, that leads to a huge bias because there are many more values equal to one due to rounding errors than values equal to zero.