# [R] Puzzled by the behaviour of rbinom().

Rolf Turner r@turner @end|ng |rom @uck|@nd@@c@nz
Sat Jul 30 01:36:41 CEST 2022

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In a certain arcane context I wanted to look at the result of
applying rbinom() to two versions of the probability argument,
the versions differing in only a small number (three) of entries.

I thought that if I called set.seed() (with the same argument) prior to
each call to rbinom(), I would get results that differed only where the
probabilities differed.  Most of the time this appears to be true:

set.seed(17) # Or any other seed, in my experience.
p0 <- runif(147)
p1 <- p0
p1[c(26,65,131)] <- 0.5
set.seed(42)
r0 <- rbinom(147,1000,p0)
set.seed(42)
r1 <- rbinom(147,1000,p1)
which(r1 != r0)
  26  65 131

But there is a particular probability vector for which the expected
result does not hold.  I have attached this vector in a file
p.weird.txt.  Access it via p.weird <- dget("p.weird.txt").

If I do:

p0 <- p.weird
p1 <- p0
p1[c(26,65,131)] <- 0.5
set.seed(42)
r0 <- rbinom(147,1000,p0)
set.seed(42)
r1 <- rbinom(147,1000,p1)
which(r1 != r0)

then I get

  26  65  66  72  73  74  75  76 131

so the results differ (inexplicably, to me) at indices 66, 72, 73, 74,
75, and 76 as well as at the indices at which they would be
expected to differ.

There is "pattern" or "structure" in p.weird (try plot(p.weird) to
see it) but why should that matter?

I have just now discerned that if I (slightly) *round* the values of
p.weird:

p.round <- round(p.weird,12)

then going through the rbinom() exercise with p.round gives the
expected results, i.e. r0 and r1 differ only at indices 26, 65 and 131.

Note that although p.round and p.weird are "slightly different":

> > range(p.round-p.weird)
>  -4.749534e-13  4.686251e-13

they differ by less than sqrt(.Machine\$double.eps) whence all.equal()
says that they are "the same".

I am completely unable to understand how there could be a mechanism by
which the behaviour of rbinom() would be affected in this way.

Can anyone provide me with enlightenment?  Ta.

cheers,

Rolf Turner

--
Honorary Research Fellow
Department of Statistics
University of Auckland
Phone: +64-9-373-7599 ext. 88276

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