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Generate random numbers under constrain

7 messages · Ragia Ibrahim, Bert Gunter, Boris Steipe +2 more

Original
Ragia Ibrahim
# 
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
Bert Gunter
# 
Well, if their sum must be < 1 they ain't random...

But anyway... given n

randnums <- function(n)
{


Bert Gunter
Genentech Nonclinical Biostatistics
(650) 467-7374

"Data is not information. Information is not knowledge. And knowledge
is certainly not wisdom."
Clifford Stoll
On Sat, Nov 22, 2014 at 6:29 AM, Ragia Ibrahim <ragia11 at hotmail.com> wrote:
Bert Gunter
# 
(Hit send key by accident before I was finished ...)

Bert Gunter
Genentech Nonclinical Biostatistics
(650) 467-7374

"Data is not information. Information is not knowledge. And knowledge
is certainly not wisdom."
Clifford Stoll
On Sat, Nov 22, 2014 at 7:14 AM, Bert Gunter <bgunter at gene.com> wrote:
But anyway, one way is ... given n

 randnums <- function(n)
 {
u <- runif(n)
u/sum(u)
}

 Bert Gunter
Boris Steipe
# 
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:

            

      
      
      
    

        

      
      
    

  
  


  


      

    

    

      
      

        


  

        

      Ranjan Maitra
    

    

      
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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:

        

            

      
      
      
    

        

      
      
    

            

      
      
      
    

        

      
      
    

        

  
    

      
      
    

  


  


      

    

    

      
      

        


  

        

      Boris Steipe
    

    

      
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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:

        

            

      
      
      
    

        

      
      
    

            

      
      
      
    

        

      
      
    

            

      
      
      
    

        

      
      
    

  
  


  


      

    

    

      
      

        


  

        

      David Winsemius
    

    

      
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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))