Random Problems with R

with Philip B. Stark

R (Version 3.5.1 patched) has two issues with its random sampling function- ality. First, it uses a version of the Mersenne Twister known to have a seed- ing problem, which was corrected by the authors of the Mersenne Twister in 2002. Updated C source code is available at http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/MT2002/CODES/mt19937ar.c. Second, R generates random integers between $1$ and $m$ by multiplying random floats by $m$, taking the floor, and adding $1$ to the result. Well-known quantization effects in this approach result in a non-uniform distribution on ${1, \ldots, m}$. The difference, which depends on $m$, can be substantial. Because the sample function in R relies on generating random integers, random sampling in R is biased. There is an easy fix: construct random integers directly from random bits, rather than multiplying a random float by m. That is the strategy taken in Python’s numpy.random.randint() function, and recommended by the authors of the Mersenne Twister algorithm, among others. Example source code in Python is available at https://github.com/statlab/cryptorandom/blob/master/cryptorandom/cryptorandom.py (see functions getrandbits() and randbelow_from_randbits()).