I don't understand this discussion at all. n random numbers constrained to have sum <=1 are still random. They are not all independent. That said, the original poster's question is ill=formed since there can be multiple distributions these random numbers come from. best wishes, Ranjan On Sat, 22 Nov 2014 10:29:18 -0500 Boris Steipe <boris.steipe at utoronto.ca> wrote:> These are contradictory requirements: either you have n random numbers from the interval [0,1), then you can't guarantee anything about their sum except that it will be in [0,n). Or you constrain the sum, then your random numbers cannot be random in [0,1). You could possibly scale the random numbers: > n <- 13 > x <- runif(n) > x <- x / sum(x) > x; sum(x) > > This will guarantee that their sum is 1 (to numerical accuracy), but your numbers are then effectively drawn from the interval [0,2/n) for large n. > > B. > > > On Nov 22, 2014, at 9:29 AM, Ragia Ibrahim <ragia11 at hotmail.com> wrote: > > > > > Dear all, > > I use R 3.1.1 for Windows. > > kindly how can I generate n number of random numbers with probability from [0,1] > > and their sum must not be more than one > > thanks in advance > > Ragia > > > > > > > > [[alternative HTML version deleted]] > > > > ______________________________________________ > > R-help at r-project.org mailing list > > https://stat.ethz.ch/mailman/listinfo/r-help > > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > > and provide commented, minimal, self-contained, reproducible code. > > ______________________________________________ > R-help at r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. >-- Important Notice: This mailbox is ignored: e-mails are set to be deleted on receipt. Please respond to the mailing list if appropriate. For those needing to send personal or professional e-mail, please use appropriate addresses. ____________________________________________________________ FREE ONLINE PHOTOSHARING - Share your photos online with your friends and family! Visit http://www.inbox.com/photosharing to find out more!
Of course they are random. But they can't all be randomly picked from [0,1). By scaling them, one is effectively scaling the interval from which they are picked. B. Nb: the scaling procedure will work for any probability distribution. On Nov 22, 2014, at 10:54 AM, Ranjan Maitra <maitra.mbox.ignored at inbox.com> wrote:> I don't understand this discussion at all. > > n random numbers constrained to have sum <=1 are still random. They are not all independent. > > That said, the original poster's question is ill=formed since there can be multiple distributions these random numbers come from. > > best wishes, > Ranjan > > > > On Sat, 22 Nov 2014 10:29:18 -0500 Boris Steipe <boris.steipe at utoronto.ca> wrote: > >> These are contradictory requirements: either you have n random numbers from the interval [0,1), then you can't guarantee anything about their sum except that it will be in [0,n). Or you constrain the sum, then your random numbers cannot be random in [0,1). You could possibly scale the random numbers: >> n <- 13 >> x <- runif(n) >> x <- x / sum(x) >> x; sum(x) >> >> This will guarantee that their sum is 1 (to numerical accuracy), but your numbers are then effectively drawn from the interval [0,2/n) for large n. >> >> B. >> >> >> On Nov 22, 2014, at 9:29 AM, Ragia Ibrahim <ragia11 at hotmail.com> wrote: >> >>> >>> Dear all, >>> I use R 3.1.1 for Windows. >>> kindly how can I generate n number of random numbers with probability from [0,1] >>> and their sum must not be more than one >>> thanks in advance >>> Ragia >>> >>> >>> >>> [[alternative HTML version deleted]] >>> >>> ______________________________________________ >>> R-help at r-project.org mailing list >>> https://stat.ethz.ch/mailman/listinfo/r-help >>> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html >>> and provide commented, minimal, self-contained, reproducible code. >> >> ______________________________________________ >> R-help at r-project.org mailing list >> https://stat.ethz.ch/mailman/listinfo/r-help >> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html >> and provide commented, minimal, self-contained, reproducible code. >> > > > -- > Important Notice: This mailbox is ignored: e-mails are set to be deleted on receipt. Please respond to the mailing list if appropriate. For those needing to send personal or professional e-mail, please use appropriate addresses. > > ____________________________________________________________ > FREE ONLINE PHOTOSHARING - Share your photos online with your friends and family! > Visit http://www.inbox.com/photosharing to find out more! > > ______________________________________________ > R-help at r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code.
In the 2 and 3 vector case it is possible do define a fairly simple sampling space where this is possible. Consider the unit square where the sample space is the area where x+y <1. It generalizes to 3 dimensions with no difficulty. x= (0:100)/100 y= (0:100)/100 z=outer(x,y, function(x,y) 1-x-y) library(lattice) wireframe(z~x+y, data.frame(x=x,y=rep(y,each=101), z) ,zlim=c(0,1) , scales=list(arrows=FALSE)) So I think the OP _is_ asking for a _random_ variable drawn from a sample space in an n-dimensional hyper-"triangular pyramid", with base being the n-1 dimensional analogue of an equilateral regular triaggle and the height of the pyramid being some value that corresponds to a value of 1-(nthroot(of some sum( that I cannot state with clarity right now)) -- David. On Nov 22, 2014, at 8:01 AM, Boris Steipe wrote:> Of course they are random. But they can't all be randomly picked from [0,1). > By scaling them, one is effectively scaling the interval from which they are picked. > > B. > Nb: the scaling procedure will work for any probability distribution. > > > > On Nov 22, 2014, at 10:54 AM, Ranjan Maitra <maitra.mbox.ignored at inbox.com> wrote: > >> I don't understand this discussion at all. >> >> n random numbers constrained to have sum <=1 are still random. They are not all independent. >> >> That said, the original poster's question is ill=formed since there can be multiple distributions these random numbers come from. >> >> best wishes, >> Ranjan >> >> >> >> On Sat, 22 Nov 2014 10:29:18 -0500 Boris Steipe <boris.steipe at utoronto.ca> wrote: >> >>> These are contradictory requirements: either you have n random numbers from the interval [0,1), then you can't guarantee anything about their sum except that it will be in [0,n). Or you constrain the sum, then your random numbers cannot be random in [0,1). You could possibly scale the random numbers: >>> n <- 13 >>> x <- runif(n) >>> x <- x / sum(x) >>> x; sum(x) >>> >>> This will guarantee that their sum is 1 (to numerical accuracy), but your numbers are then effectively drawn from the interval [0,2/n) for large n. >>> >>> B. >>> >>> >>> On Nov 22, 2014, at 9:29 AM, Ragia Ibrahim <ragia11 at hotmail.com> wrote: >>> >>>> >>>> Dear all, >>>> I use R 3.1.1 for Windows. >>>> kindly how can I generate n number of random numbers with probability from [0,1] >>>> and their sum must not be more than one >>>> thanks in advance >>>> Ragia >>>> >>>> >>>> >>>> [[alternative HTML version deleted]] >>>> >>>> ______________________________________________ >>>> R-help at r-project.org mailing list >>>> https://stat.ethz.ch/mailman/listinfo/r-help >>>> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html >>>> and provide commented, minimal, self-contained, reproducible code. >>> >>> ______________________________________________ >>> R-help at r-project.org mailing list >>> https://stat.ethz.ch/mailman/listinfo/r-help >>> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html >>> and provide commented, minimal, self-contained, reproducible code. >>> >> >> >> -- >> Important Notice: This mailbox is ignored: e-mails are set to be deleted on receipt. Please respond to the mailing list if appropriate. For those needing to send personal or professional e-mail, please use appropriate addresses. >> >> ____________________________________________________________ >> FREE ONLINE PHOTOSHARING - Share your photos online with your friends and family! >> Visit http://www.inbox.com/photosharing to find out more! >> >> ______________________________________________ >> R-help at r-project.org mailing list >> https://stat.ethz.ch/mailman/listinfo/r-help >> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html >> and provide commented, minimal, self-contained, reproducible code. > > ______________________________________________ > R-help at r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code.David Winsemius Alameda, CA, USA