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

[Duncan Murdoch]

To sample uniformly from -A to A is impossible in R, because R only 
deals with a tiny subset of those numbers when A > 0.

However, as computational statisticians, we're all quite used to 
pretending that runif(n, -1, 1) samples uniformly from -1 to 1, even 
though it gives a sample on a discrete subset of the interval. For most 
purposes that's a good enough approximation.

So if you want to sample from -A to A, just multiply the result above by A:

  A * runif(n, -1, 1)

This produces a pretty good approximation to the required result even 
when A == Inf. You'll only get 3 values:  -Inf, NaN, Inf (and might not 
see any NaN values, which arise when runif(n, -1, 1) gives an exact 0).

I say that's a good approximation, because if you want samples uniformly 
distributed on -A to A, you should only get values that would be 
represented by +/- Inf in R in the limit as A -> Inf.

Duncan Murdoch

On 2025-07-28 2:01 p.m., Rui Barradas wrote:
> On 7/28/2025 5:30 PM, Daniel Lobo wrote:
>> Many thanks for your guidance. However my original problem is, how to
>> select n points in the Real line randomly without any preference of
>> any particular probability distribution?
>>
>> On Mon, 28 Jul 2025 at 21:45, Rui Barradas <ruipbarradas using sapo.pt> wrote:
>>>
>>> On 7/28/2025 5:00 PM, Daniel Lobo 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?
>>>>
>>>> ______________________________________________
>>>> 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.
>>> Hello,
>>>
>>>
>>> What you are asking doesn't make sense.
>>> The uniform distribution's PDF is
>>>
>>> f(x;a, b) = 1/abs(b - a) if x in [a, b]
>>>                0            otherwise
>>>
>>> So what you have is 1/abs(Inf - -Inf) = 1/abs(Inf) = 0.
>>>
>>> And the cumulative distribution function is even worse, it will give you
>>> the indeterminate Inf/Inf.
>>> See the Wikipedia on the uniform distribution [1].
>>>
>>>
>>> [1] https://en.wikipedia.org/wiki/Continuous_uniform_distribution
> Hello,
> 
> Here is another explanation on the reason why you should sample from
> finite limits that make sense [1].
> 
> Ben's answer points you in an acceptable direction. Here is the same
> idea with other limits meant to get better floating-point accuracy.
> 
> 
> n <- 1e6  # change this at will
> 
> mm <- .Machine$double.xmax
> u <- runif(n, min =  -mm/3, max = mm/3)
> hist(u)
> 
> 
> [1]
> https://math.stackexchange.com/questions/3784691/probability-distribution-of-choosing-a-real-number-at-random
> 
> Hope this helps,
> 
> Rui Barradas
> 
> ______________________________________________
> 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.