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

[Duncan Murdoch]

As others have told you, you can't.  You can talk about a uniform 
distribution on the reals but there's no way to normlize it so it 
integrates to 1, so it's an "improper" distribution, and there is no way 
to sample from those.

Duncan Murdoch

On 2025-07-28 12:30 p.m., 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?
>>>
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>> 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
> 
> ______________________________________________
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> and provide commented, minimal, self-contained, reproducible code.