Random problems with R

TL;DR

This paper identifies a bias in R's random sampling method due to quantization effects, and proposes a fix by generating random integers directly from random bits, improving sampling uniformity.

Contribution

It highlights the bias in R's current random integer generation and introduces a simple, effective method to produce unbiased random samples using random bits.

Findings

R's current method causes non-uniform distributions in sampling.

Using random bits for integer generation reduces bias.

Python's numpy.random.randint() employs this improved approach.

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 https://github.com/statlab/cryptorandom/blob/master/cryptorandom/cryptorandom.py (see functions getrandbits() and randbelow_from_randbits()).