I think I see the rub: You would like to see the distribution of a sample be identical to the distribution from which it was sampled. But if it is random then that can happen only in the long run, not on every sample. That is why samples from a normal density are *not* themselves normal - they're "t." When the sample size is large enough the differences between a random sample's density and its parent density become vanishingly small. Thus the differences you observe from repeated random samples from the binomial. Repeated sampling produces slightly different numbers of successes. How could it be otherwise?
Charles Annis, P.E. [EMAIL PROTECTED] phone: 561-352-9699 eFax: 614-455-3265 http://www.StatisticalEngineering.com ________________________________________ From: Philip Twumasi-Ankrah [mailto:[EMAIL PROTECTED] Sent: Wednesday, May 28, 2008 10:36 AM To: [EMAIL PROTECTED] Subject: RE: [R] "rbinom" : Does randomness preclude precision? Charles, When you simulate data from a distribution, what you effect are doing is generating a sequence of values that would correspond to that distribution. So you can generate 1000 values from a normal distribution and expect that when you check on the distribution of your sample (what you do with your qqnorm or Q-Q plot), it should be a close fit with the theoretical distribution with the assigned parameter values. It will be difficult to explain why a simulated data may be different from the distribution it is was generated from . I think you can not blame it on randomness. I hope you understand what I am trying to determine. "Charles Annis, P.E." <[EMAIL PROTECTED]> wrote: What do you mean by "... *eventual* nature of the distribution?" If you simulated 100 samples, would you expect to see 1.5 successes? Or 1? Or 2? How many, in your thinking, is "eventual?" Charles Annis, P.E. [EMAIL PROTECTED] phone: 561-352-9699 eFax: 614-455-3265 http://www.StatisticalEngineering.com -----Original Message----- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Philip Twumasi-Ankrah Sent: Wednesday, May 28, 2008 9:52 AM To: [EMAIL PROTECTED] Cc: r-help@r-project.org Subject: Re: [R] "rbinom" : Does randomness preclude precision? Teds reply is a bit comforting and as indicated in my post, I am resorting to using "sample" but as an academic issue, does randomness preclude precision? Randomness should be in the sequence of zeros and ones and how they are simulated at each iteration of the process but not in the eventual nature of the distribution. I mean if I simulated a Normal (0, 1) and got a Normal(1.5, 2) these would be very different distributions. It is the same with simulating a Binomial(1, p=0.15) and getting Binomial(1, 0.154) [EMAIL PROTECTED] wrote: On 28-May-08 12:53:26, Philip Twumasi-Ankrah wrote: > I am trying to simulate a series of ones and zeros (1 or 0) and I am > using "rbinom" but realizing that the number of successes expected is > not accurate. Any advice out there. > > This is the example: > > N<-500 > status<-rbinom(N, 1, prob = 0.15) > count<-sum(status) > > 15 percent of 500 should be 75 but what I obtain from the "count" > variable is 77 that gives the probability of success to be 0.154. Not > very good. The difference (77 - 75 =2) is well within the likely sampling variation when 500 values are sampled independently with P(1)=0.15: The standard deviation of the resulting number of 1s is sqrt(500*0.15*0.85) = 7.98, so the difference of 2 is only 1/4 of a standard deviation, hence very likely to be equalled or exceeded. Your chance of getting exactly 75 by this method is quite small: dbinom(75,500,0.15) [1] 0.04990852 and your chance of being 2 or more off your target is 1 - sum(dbinom((74:76),500,0.15)) [1] 0.8510483 > Is there another way beyond using "sample" and "rep" together? It looks as though you are seeking to obtain exactly 75 1s, randomly situated, the rest being 0s, so in effect you do need to do something on the lines of "sample" and "rep". Hence, something like status <- rep(0,500) status[sample((1:500),75,replace=FALSE)] <- 1 Hoping this helps, Ted. -------------------------------------------------------------------- E-Mail: (Ted Harding) Fax-to-email: +44 (0)870 094 0861 Date: 28-May-08 Time: 14:19:24 ------------------------------ XFMail ------------------------------ A Smile costs Nothing But Rewards Everything Happiness is not perfected until it is shared -Jane Porter [[alternative HTML version deleted]] ______________________________________________ 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. A Smile costs Nothing But Rewards Everything Happiness is not perfected until it is shared -Jane Porter ______________________________________________ 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.
