[R] ties in runif() output

Prof Brian Ripley ripley at stats.ox.ac.uk
Sat Jun 26 08:15:17 CEST 2004

On Fri, 25 Jun 2004, Douglas Grove wrote:

> I get ties in output from runif() when I generate as few as 10^5
> variates and get quite a lot when I generate 10^6.  Is this 
> expected??  

It should have been.

> I haven't seen any duplication with rnorm(10^6), but
> see varying amounts of duplication using rexp(), rbeta() and
> rgamma().  I would have thought that there'd be enough precision
> that one wouldn't get ties until generating samples larger than this..

Did you do the calculations?  Please do so. There are about 2e9 possible
values of the standard generators.

> qbirthday(classes=2e9)
[1] 52655

Statisticians ought to know about the birthday problem!

(rnorm is different because the default generator uses two uniforms, 
deliberately to increase the precision.)

> > set.seed(222)
> > sum(duplicated(runif(10^5)))
> [1] 4

That's unusually high, BTW.

> > sum(duplicated(runif(10^6)))
> [1] 140

Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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