R help - Jul 2025 - Drawing random numbers from Uniform distribution with infinite range

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 at 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 at 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

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 at 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 at 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
> 
> ______________________________________________
> R-help at 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.

Why? What do you plan to do with those numbers? I think that was Ben's
point: perhaps there is a different approach to accomplishing what you
want to accomplish. What do you want to accomplish?

--Chris Ryan

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 at 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?
>>>
>

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 at 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 at 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

If you think a bit, the requirement is silly.  In computers, "real
numbers"
are not a real thing. They are approximations with limits in several ways,
and some of these limits cannot be surmounted except perhaps someday with
quantum computers which may extend the range but are not likely to totally
do what you ask.

Pick a bizarrely large number such as a googolplex ( ten raised to the
googol power) and ask what a typical number chosen between 0 and this
selected number is? A typical number, say an integer,  is not likely to be
in the miniscule range of 0 to the amount an integer on your machine holds.
Even if you use python-style extended integers, which are not a normal part
of R, the number of digits in such a random number may exceed the memory
available on your machine, or even the combined machines on our planet.
Picking a small enough number of something like -1,000,000,000 to 1,000,000,
000 has a probably approaching zero. Even using floating point in something
like 64 bits is rapidly overwhelmed.

Now, substitute a limit of infinity and negative infinity into the problem.
In a mathematical sense, the average number chosen between say zero and
infinity would be the nonsensical value of ?/2 which is also ?. Picking N
values between -? and +? does not seem helpful for almost any purpose. The
results cannot be graphed for example.

And, picking a random number between zero and one can be magnified only up
to a point as the number of valid digits is limited.

And, as many have pointed out, when you leave the Platonic Mathematical
universe and descend to using ANY computer language, such as R, the only
valid large value that the machine can handle is ? itself, not as a
measured amount, but as a concept.

Would your need be met by simply choosing large numbers for the range that
do not propagate infinities in the software but are representative enough?
As noted by others, you at least may need to stay under half the largest
number a machine allows unless you use a package supporting indefinite
precision numbers. But then, built-in functions are not expected to support
these numbers. The mathematics of density functions suggests that the
probability of choosing something specific like pi to infinite digits in an
infinite distribution is zero as 1/? is mathematically zero.

I am curious what reason you have chosen to work on this problem and wonder
if a more carefully chosen set of requirements meet your need.


-----Original Message-----
From: R-help <r-help-bounces at r-project.org> On Behalf Of Daniel Lobo
Sent: Monday, July 28, 2025 12:30 PM
To: Rui Barradas <ruipbarradas at sapo.pt>
Cc: r-help at r-project.org
Subject: Re: [R] Drawing random numbers from Uniform distribution with
infinite range

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 at 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 at 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
______________________________________________
R-help at 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.

There are an infinite number of values between 0 and 1. Likewise between any two
values, though it might get tricky if they were infinitely close together. The
real numbers also go from negative infinity to positive infinity. Computers have
limited memory that can handle a minute portion of this range.

There is also an issue with random number generator. Most computer random number
generators are pseudo-random. That is they are "random" with some
range, but expanding beyond that range they show patterns. There are services
that will provide true random numbers (e.g. https://www.random.org/), but there
may be limits to the rate the numbers are generated or provided to you.

"without preference of any particular probability distribution" but
the Uniform distribution is a probability distribution.

All computer numbers are discrete. If the computer can process 17 decimal
places, then anything in the twentieth decimal place will be lost. If your
computer can handle 30 decimal places, then anything in the fiftieth decimal
place will be lost. This results in number gaps between consecutive values at
the smallest significant digit. So even a Uniform distribution where every value
has equal probability of being chosen is not true for values between consecutive
least significant digit.

Significant digits is not decimal places. 12345654678239543 is 17 digits as is.
0. 1234565467823954. However, 12345654678239543.1234565467823954 is 34 digits.
Also, 123456546782395430000000 can be a stored number in the computer but if
accuracy is 17 digits then the trailing zeros will always be zero (or some
random noise). A program like R can handle very large and small numbers, but not
every digit will be kept in memory.

Things get more complex in that the computer must store things in binary. Not
all real numbers have a finite binary equivalent. This can make a simple program
give unexpected outcomes.

options(digits=20)
for (i in 1:100) {
  j <- 1 + 0.1^i
  if (j == 1) {
    cat("At i =", i, "-> 1 + 0.1^i == 1 (difference lost due
to precision)\n")
  } else {
    cat("i =", i, "j =", j, "\n")
  }
}

Everything looks good up until options=16. At options=17 the results are
different.
There are programming strategies to overcome this limit, but there is still a
limit.

library(Rmpfr)
precBits <- 256  # bits of precision (~77 decimal digits)
for (i in 1:50) {
  small <- mpfr("0.1", precBits)^i
  j <- 1 + small
  if (j == 1) {
    cat("At i =", i, "j == 1 (even with high precision)\n")
    break
  } else {
    cat("i =", i, "j =", format(j, digits = 40),
"\n")
  }
}

Eventually, you run out of computer memory. If this is a part of a large process
the execution time may be long.

Tim



-----Original Message-----
From: R-help <r-help-bounces at r-project.org> On Behalf Of Daniel Lobo
Sent: Monday, July 28, 2025 12:30 PM
To: Rui Barradas <ruipbarradas at sapo.pt>
Cc: r-help at r-project.org
Subject: Re: [R] Drawing random numbers from Uniform distribution with infinite
range

[External Email]

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 at 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 at r-project.org mailing list -- To UNSUBSCRIBE and more, see
> > https://st/
> >
at.ethz.ch%2Fmailman%2Flistinfo%2Fr-help&data=05%7C02%7Ctebert%40ufl
> > .edu%7Cef232b26cd0a45cb285f08ddcdf70798%7C0d4da0f84a314d76ace60a6233
> > 1e1b84%7C0%7C0%7C638893183054544956%7CUnknown%7CTWFpbGZsb3d8eyJFbXB0
> > eU1hcGkiOnRydWUsIlYiOiIwLjAuMDAwMCIsIlAiOiJXaW4zMiIsIkFOIjoiTWFpbCIs
> >
IldUIjoyfQ%3D%3D%7C0%7C%7C%7C&sdata=IraxT8iu7WasjesdmwC3KXg7qXjxaQJL
> > WER%2FGenW%2BRs%3D&reserved=0 PLEASE do read the posting guide
> > https://ww/
> >
w.r-project.org%2Fposting-guide.html&data=05%7C02%7Ctebert%40ufl.edu
> > %7Cef232b26cd0a45cb285f08ddcdf70798%7C0d4da0f84a314d76ace60a62331e1b
> > 84%7C0%7C0%7C638893183054560855%7CUnknown%7CTWFpbGZsb3d8eyJFbXB0eU1h
> > cGkiOnRydWUsIlYiOiIwLjAuMDAwMCIsIlAiOiJXaW4zMiIsIkFOIjoiTWFpbCIsIldU
> >
IjoyfQ%3D%3D%7C0%7C%7C%7C&sdata=%2FrlPXP%2BCnUQ1S5yBOBaf3zj71vrQYF9m
> > cJ8woJ0QI60%3D&reserved=0 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.w/
> ikipedia.org%2Fwiki%2FContinuous_uniform_distribution&data=05%7C02%7Ct
> ebert%40ufl.edu%7Cef232b26cd0a45cb285f08ddcdf70798%7C0d4da0f84a314d76a
> ce60a62331e1b84%7C0%7C0%7C638893183054570228%7CUnknown%7CTWFpbGZsb3d8e
> yJFbXB0eU1hcGkiOnRydWUsIlYiOiIwLjAuMDAwMCIsIlAiOiJXaW4zMiIsIkFOIjoiTWF
> pbCIsIldUIjoyfQ%3D%3D%7C0%7C%7C%7C&sdata=bimbtz4%2BHqya58n4A1CVpHsWZ4I
> 1hoDq25gY7z81HII%3D&reserved=0
______________________________________________
R-help at 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.

R can only represent representable numbers.
The cardinality of the set of numbers that could be the result of
sampling in R is
some finite number a bit less than 2^64.  It's not even countably infinite.
The real line is UNcountably infinite.
Almost no points on the real line can be represented.

Second, any random selection from any set is going to be
according to *some* probability distribution.  The whole without any
preference for any particular probability distribution" makes no sense.
(Can you possibly be thinking of Bayesian 'improper priors'?)

Bearing in mind the finiteness of representable numbers and the
intrinsic necessity of having *some* probability distribution,
why do you think you need to do this thing that cannot be done?

On Tue, 29 Jul 2025 at 04:51, Daniel Lobo <danielobo9976 at gmail.com>
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 at 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 at 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
>
> ______________________________________________
> R-help at 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.