R help - Jul 2011 - Random number generation

Hi, 

I want to generate multiple sets of random numbers.
The requirement is that:
1) each set have 3 random numbers;
2) the sum of the three number is always 1.

how to do this?

thank you,

karena

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On 07/21/2011 07:18 PM, karena wrote:
> Hi,
>
> I want to generate multiple sets of random numbers.
> The requirement is that:
> 1) each set have 3 random numbers;
> 2) the sum of the three number is always 1.
>
> how to do this?
Try this:

     df<-data.frame(a=runif(10),b=runif(10))
     df$c=df$a+df$b
     df

Replace 10 with the number of rows that you want. Replace runif with 
your random function of choice.

Jason

On 21/07/2011 7:18 PM, karena wrote:
> Hi,
>
> I want to generate multiple sets of random numbers.
> The requirement is that:
> 1) each set have 3 random numbers;
> 2) the sum of the three number is always 1.
>
> how to do this?
There are lots of ways.  What is the context?  It would determine the 
first two steps:

1.  Generate A.
2.  Generate B.
3.  C <- 1-A-B

Duncan Murdoch

Could this possibly be a homework question?

     cheers,

         Rolf Turner

On 22/07/11 11:18, karena wrote:
> Hi,
>
> I want to generate multiple sets of random numbers.
> The requirement is that:
> 1) each set have 3 random numbers;
> 2) the sum of the three number is always 1.
>
> how to do this?

Hi:

Here's one way using uniform(0, 1) pseudo-random numbers, but there
are many ways you could go about this.

# each row comprises a set of three pseudo-random numbers
u <- matrix(runif(30), nrow = 10)
# divide each element in a row by its row sum
v <- t(apply(u, 1, function(x) x/sum(x)))
rowSums(v)
 [1] 1 1 1 1 1 1 1 1 1 1

# An equivalent way (about equally fast) is
u/outer(rowSums(u), rep(1, 3))

Now try

hist(unlist(v))

and notice that the distribution of the constrained sets is not really
uniform. This is a consequence of setting a constraint on the sum of
each sample. Another way to see this is to plot

plot(sort(unlist(v)))

A 'truly' uniform random sample would lie approximately on a straight
line in this plot.

It would seem to me that a better approach would be to sample from a
simplex embedded in the unit cube. I'd suggest looking into the
compositions package (because you are effectively generating
compositional data) and look into its capabilities. At least a couple
of the references in the package's overview page seem to be germane to
the problem.
The pair of runif.* functions appear to be relevant.

HTH,
Dennis



On Thu, Jul 21, 2011 at 4:18 PM, karena <dr.jzhou at gmail.com>
wrote:
> Hi,
>
> I want to generate multiple sets of random numbers.
> The requirement is that:
> 1) each set have 3 random numbers;
> 2) the sum of the three number is always 1.
>
> how to do this?
>
> thank you,
>
> karena
>
> --
> View this message in context:
http://r.789695.n4.nabble.com/Random-number-generation-tp3685463p3685463.html
> Sent from the R help mailing list archive at Nabble.com.
>
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