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-boun...@r-project.org> On Behalf Of Daniel Lobo Sent: Monday, July 28, 2025 12:30 PM To: Rui Barradas <ruipbarra...@sapo.pt> Cc: r-help@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 <ruipbarra...@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@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@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-help@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.
