Hi Peng, Does this help? sum(diff(c(0,sort(sample(seq(1,99,1),50,replace=T)),100))) Regards Alex
-----Original Message----- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Peng Jiang Sent: July 8, 2008 3:57 AM To: [EMAIL PROTECTED] Cc: [EMAIL PROTECTED] Subject: Re: [R] Sum(Random Numbers)=100 Hi, I am afraid there is no other way except using brute force, that is , loop until their sum reaches your expectation. it is easy to figure out this probability by letting their sum to be a new random variable Z and Z = X_1 + \ldots + X_n where X_i ~ Poisson({\lambda}_i) . By calculating their moment generate function we can find the pmf of Z which is a new Poisson random variable with the parameter \sum_{i}{{\lambda}_i}. and Moshe Olshansky's method is also correct except it is based on the conditioning. On 2008-7-8, at 下午1:58, Shubha Vishwanath Karanth wrote: On 2008-7-8, at 下午2:39, Moshe Olshansky wrote: > 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 > <[EMAIL PROTECTED] > > wrote: > >> From: Shubha Vishwanath Karanth <[EMAIL PROTECTED]> >> Subject: [R] Sum(Random Numbers)=100 >> To: [EMAIL PROTECTED] >> 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@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@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. ----------------------------------------------- Peng Jiang 江鹏 ,Ph.D. Candidate Antai College of Economics & Management 安泰经济管理学院 Department of Mathematics 数学系 Shanghai Jiaotong University (Minhang Campus) 800 Dongchuan Road 200240 Shanghai P. R. China ______________________________________________ R-help@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@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.
