Title: Random problems with R,
Abstract: R (Version 3.5.1 patched) has an issue with its random sampling
functionality. 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, among others. Example source code in Python is available at
this https URL
(see functions getrandbits() and randbelow_from_randbits()).