[Rd] Bias in R's random integers?
Duncan Murdoch
murdoch@dunc@n @ending from gm@il@com
Thu Sep 20 18:03:02 CEST 2018
On 20/09/2018 11:01 AM, Radford Neal wrote:
>> From: Duncan Murdoch <murdoch.duncan using gmail.com>
>
>> Let's try it:
>>
>> > m <- (2/5)*2^32
>> > m > 2^31
>> [1] FALSE
>> > x <- sample(m, 1000000, replace = TRUE)
>> > table(x %% 2)
>>
>> 0 1
>> 399850 600150
>>
>> Since m is an even number, the true proportions of evens and odds should
>> be exactly 0.5. That's some pretty strong evidence of the bug in the
>> generator.
>
>
> It seems to be a recently-introduced bug. Here's output with R-2.15.1:
>
> R version 2.15.1 (2012-06-22) -- "Roasted Marshmallows"
> Copyright (C) 2012 The R Foundation for Statistical Computing
> ISBN 3-900051-07-0
> Platform: x86_64-unknown-linux-gnu (64-bit)
>
> R is free software and comes with ABSOLUTELY NO WARRANTY.
> You are welcome to redistribute it under certain conditions.
> Type 'license()' or 'licence()' for distribution details.
>
> R is a collaborative project with many contributors.
> Type 'contributors()' for more information and
> 'citation()' on how to cite R or R packages in publications.
>
> Type 'demo()' for some demos, 'help()' for on-line help, or
> 'help.start()' for an HTML browser interface to help.
> Type 'q()' to quit R.
>
> > set.seed(123)
> > m <- (2/5)*2^32
> > m > 2^31
> [1] FALSE
> > x <- sample(m, 1000000, replace = TRUE)
> > table(x %% 2)
>
> 0 1
> 499412 500588
>
> So I doubt that this has anything to do with bias from using 32-bit
> random values.
There are two bugs, one recent one (allowing fractional m to slip
through) and one old one (the bias). The test above shows the bias with
m+1, i.e. in R 2.15.1
> x <- sample(m + 1, 1000000, replace = TRUE)
> table(x %% 2)
0 1
466739 533261
and you can see it in the original m with
x <- sample(m, 1000000, replace = TRUE)
plot(density(x[x %% 2 == 0]))
Duncan Murdoch
More information about the R-devel
mailing list