On 28-Sep-09 12:15:39, Joerg van den Hoff wrote: > this is probably not really a R specific question, if so apologies > for off-topic posting: > > I'm interested in the probability density function of the maximum > values from repeated samples of size N from a normal distribution: > > smp <- rnorm(N, meanval, stdev) > > with some mean 'meanval' and standard deviation 'stdev'. > > I would like to know what is the frequency distribution of max(smp) if > I draw many such > samples? > > if I investigate this simply via a simulation, I get of course > approximate > results (and see that the resulting distribution is not quite normal > anymore, that the mean increases with increasing N, etc.). > > my question: does somebody know whether there exists an analytical > expression for the distribution of max(smp) (or where to look)? > > thanks, > joerg
Let Pmax(x,N) be the probability that the maximum of N is <= x. Pmax(x,N) = Prob(all N values <= x) = (Prob(a single value <= x))^N = (pnorm(x,meanval,stdev))^N Hence the frequency distribution is the derivative of this with respect to x, say pmax(x,N): pmax(x,N) = N*((pnorm(x,meanval,stdev))^(N-1))*dnorm(x,meanval,stdev) Ted. -------------------------------------------------------------------- E-Mail: (Ted Harding) <ted.hard...@manchester.ac.uk> Fax-to-email: +44 (0)870 094 0861 Date: 28-Sep-09 Time: 13:45:49 ------------------------------ XFMail ------------------------------ ______________________________________________ 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.