Needed: Understading runif() output :-)
On Thu, 25 May 2000, Prof Brian D Ripley wrote:
Yes, they are all quantized (all to ca 2^-31 or 2^-32). Reason: that's all we can assume for integer arithmetic.
Yes, indeed.
That is perfectly sufficient for a *stable* procedure for using them. As I said before, I don't think the algorithm you have for making use of them is adequate. Now, you haven't actually told us how you are generating numbers from your distribution (and you haven't actually defined the distribution precisely enough so that I could program it), but I guess you are using inversion. Don't: it is not adequate for your purposes.
Aha, now I understand! Indeed, I use inversion. My (cumulative) distribution function is F(mu) = 1 - 0.25 * mu^-2, for mu >= 0.5 and 0 for mu < 0. I have inverted it, to get the 1 / (2 * sqrt(1 - p) quantile function, then I use runif(n) for the p.
You want to make use of several random numbers if you want behaviour in the far tail. Alternatively, you could plug in a generator that had a lower quantization. The moral is a familiar one: computer results are almost always approximate, and you always have to watch out for the effects of the approximations.
Yes, it is a valuable lesson to learn. It is not that often the effects of the approximation are that glaring. I'm thinking about if I can live with this approximation in this case. I guess I should have a more thorough look into it nevertheless. My lack of training in statistics strikes again, I have based my analysis on a brief discussion in Dudewicz & Mishra's "Modern Mathematical Statistics". If someone can recommend a text that discuss this topic, I would be very happy... Best, Kjetil
Kjetil Kjernsmo Graduate astronomy-student Problems worthy of attack University of Oslo, Norway Prove their worth by hitting back E-mail: kjetikj at astro.uio.no - Piet Hein Homepage <URL:http://www.astro.uio.no/~kjetikj/> Webmaster at skepsis.no -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._