On 25-Jan-05 Weiguang Shi wrote: > Hi, > > Is there a Zipf-like distribution RNG in R? > > Thanks, > Weiguang
"Zipf's Law" (as originally formulated in studies of the frequencies of words in texts) is to the effect that the relative frequencies with which words occur once, twice, 3 times, ... are in proportion to 1/1, 1/2, 1/3, ... , 1/n, ... with no limit on n (i.e. the number of different words each represented n times is proportional to 1/n). This is "improper" since sum(1/n) = infinity, so does not define a probability distribution. A respectable analogue is Fisher's logarithmic distribution p(x) where p(x) = ((t^x)/x)/(-log(1-t)), x = 1, 2, 3, ... where t in (0,1) is the parameter of the distribution. As t -> 1, p(x+1)/p(x) -> x/(x+1) as in Zipf's Law. However, I've searched the R site and have found only one instance of a function directly related to this distribution, namely logff() in package VGAM, which is for estimating the parameter t. So it looks as though there is no direct implementation of something like "rlogdist". However, the logarithmic distribution is a limiting form of the negative binomial distribution (conditional on a positive value), and there are functions in R for random sampling from this distribution. >From my reading of "?rnbinom" in the base package, this function does not have the flexibitility you would need for this. But in the MASS package there is the function rnegbin() which does. You would need to invoke rnegbin(N, mu=..., theta=... ) where the value ... of mu is large and the value ... of theta is small, and reject cases with value zero. This of course makes it awkward to generate a sample of given size. Alternatively, you can try along the lines of > x0<-1:10000; t<-0.999; p<-((t^x0)/x0)/(-log(1-t)) > Y<-sample(x0,5000,replace=TRUE,prob=p) > hist(Y,breaks=100) While this gives the logarithmic distribution over the range of x in x0, it is inexact in that it does not permit values greater than max(x0) to be sampled. No doubt others can suggest something better than this! Best wishes, Ted. -------------------------------------------------------------------- E-Mail: (Ted Harding) <[EMAIL PROTECTED]> Fax-to-email: +44 (0)870 094 0861 [NB: New number!] Date: 25-Jan-05 Time: 10:20:57 ------------------------------ XFMail ------------------------------ ______________________________________________ [email protected] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
