[R] Drawing random numbers from Uniform distribution with infinite range

[Richard O'Keefe]

I thought I was reasonably explicit that the OP should abandon the
search for a uniform distribution on the whole real line and should
investigate transforming the problem.
If the OP really needs a distribution on the whole real line, there
are infinitely many to be had but none of them is uniform.
If the OP really needs a uniform distribution, there is one to be had
on a finite interval, and the whole real line can be bijectively
mapped onto a finite interval, just not linearly.
That remains the question of interest: what does the OP *really* need?

On Tue, 5 Aug 2025 at 22:02, peter dalgaard <pdalgd using gmail.com> wrote:
>
> Or rlogis(1e6, scale=.5) which is the same thing.
>
> But the logistic distribution is in no reasonable sense a uniform on the entire line, any more than the Gaussian is.
>
> (Some notion of a "random real" is involved in Benford's law of first digits, but that involves having a uniform distribution of log(X) and then increasing the range.)
>
> -pd
>
> > On 30 Jul 2025, at 14:11 , Richard O'Keefe <raoknz using gmail.com> wrote:
> >
> > Let's look at something that *would* work if it were not that IEEE
> > doubles are relatively small discrete set,.
> >
> > Suppose we had two things.
> > - a U(0,1) uniform random generator able to generate any *real* in the
> > range 0 .. 1
> > - an implementation of atanh() that works for any real in the range 0
> > .. 1 and can return any real number.
> > Then atanh(runif(n)*2 - 1) would do pretty much what you want,.
> > Try it in R.
> > f <- function (n = 1000000) atanh(runif(n)*2 - 1)
> > summary(f())
> > It turns out that working with *representable* numbers means that the
> > results of f() are limited to
> > roughly -18,.4 to 18.4, and with n = 1000000 the extremes are almost
> > always around 7.
> > Something that, for actual real numbers, could return *any* real, for
> > representable numbers
> > can only return -18-and-a-bit to +18-and-a-bit.
> >
> > This suggests a completely different approach to your original
> > problem, whatever it is.
> > Instead of working with the entire real line, transform your problem
> > to work with the interval (0,1).
> >
> > On Tue, 29 Jul 2025 at 04:01, Daniel Lobo <danielobo9976 using gmail.com> wrote:
> >>
> >> Hi,
> >>
> >> I want to draw a set of random number from Uniform distribution where
> >> Support is the entire Real line.
> >>
> >> runif(4, min = -Inf, max = Inf)
> >>
> >> However it produces all NAN
> >>
> >> Could you please help with the right approach?
> >>
> >> ______________________________________________
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> >> and provide commented, minimal, self-contained, reproducible code.
> >
> > ______________________________________________
> > R-help using r-project.org mailing list -- To UNSUBSCRIBE and more, see
> > https://stat.ethz.ch/mailman/listinfo/r-help
> > PLEASE do read the posting guide https://www.R-project.org/posting-guide.html
> > and provide commented, minimal, self-contained, reproducible code.
>
> --
> Peter Dalgaard, Professor,
> Center for Statistics, Copenhagen Business School
> Solbjerg Plads 3, 2000 Frederiksberg, Denmark
> Phone: (+45)38153501
> Office: A 4.23
> Email: pd.mes using cbs.dk  Priv: PDalgd using gmail.com
>