# Re: [R] Sum(Random Numbers)=100

From: Daniel Malter <daniel_at_umd.edu>
Date: Tue, 08 Jul 2008 03:13:52 -0400

what you could (what I suggest) is not technically clean because your draw is not strictly random any more. But if you want to distribute 100 on 50 units with a Poisson-distributed variable x, then your lambda must be 100/50=2. You could then sample Poisson distribution ( rpois(50,2) ), sum over all 50 values and stop as soon as the sum is exactly 100. This may take a while though. And again, this is not strictly random as you are discarding lots of distributions to achieve that.

Cheers,
Daniel

cuncta stricte discussurus

-----Ursprüngliche Nachricht-----
Von: r-help-bounces_at_r-project.org [mailto:r-help-bounces_at_r-project.org] Im Auftrag von Shubha Vishwanath Karanth
Gesendet: Tuesday, July 08, 2008 2:54 AM An: m_olshansky_at_yahoo.com; r-help_at_stat.math.ethz.ch Betreff: Re: [R] Sum(Random Numbers)=100

...actually I need to allocate certain amount of money (here I mentioned it as 100) to a randomly selected stocks(50 stocks)... i.e., 100 being divided among 50 stocks and preferably all are integer allocations(i.e., 5 8 56 12 etc without any decimals)...

Thank you,
Shubha
-----Original Message-----
From: Moshe Olshansky [mailto:m_olshansky_at_yahoo.com] Sent: Tuesday, July 08, 2008 12:09 PM
To: r-help_at_stat.math.ethz.ch; Shubha Vishwanath Karanth Subject: Re: [R] Sum(Random Numbers)=100

If they are really random you can not expect their sum to be 100. However, it is not difficult to get that given that the sum of n independent Poisson random variables equals N, any individual one has the conditional binomial distribution with size = N and p = 1/n, i.e. P(Xi=k/Sn=N) = (N over k)*(1/n)^k*((n-1)/n)^(N-k). So you can generate X1 binomial with size = 100 and p = 1/50; if X1 = k1 then the sum of the rest 49 must equal 100 - k1, so now you generate X2 binomial with size = 100-k1 and p = 1/49; if X2 = k2 then generate X3 binomial with size = 100 -(k1+k2) and p = 1/48, etc.

Why do you need this?

• On Tue, 8/7/08, Shubha Vishwanath Karanth <shubhak_at_ambaresearch.com> wrote:

> From: Shubha Vishwanath Karanth <shubhak@ambaresearch.com>
> Subject: [R] Sum(Random Numbers)=100
> To: r-help_at_stat.math.ethz.ch
> Received: Tuesday, 8 July, 2008, 3:58 PM Hi R,
>
>
>
> I need to generate 50 random numbers (preferably poisson), such that
> their sum is equal to 100. How do I do this?
>
>
>
>
>
> Thank you,
>
> Shubha
>
>
>
> This e-mail may contain confidential and/or privileged
> i...{{dropped:13}}
>
> ______________________________________________
> R-help_at_r-project.org mailing list
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This e-mail may contain confidential and/or privileged i...{{dropped:10}}

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