On 22 Mar 2004 08:36:00 -0800, [EMAIL PROTECTED] (Peter Flom) wrote: > Clearly Don is correct that it depends on the nature of the distribution > of the variable in a particular population (and on population size). > > But given a finite population, I don't think the expected value of the > maximum of a normally distributed variable is infinity. (But maybe I am > all wrong....) > > Given a population size N and a distribution, could one not bootstrap > for the maximum? I know that in the typical case, where one wants to > estimate the population parameter from a sample statiistic, the maximum > is not bootstrappable (if that's the word) but here, if we are given the > population size and the distribution, it seems to me intuitively that it > should work
Yes, there *is* such a thing as the maximum expected to be seen for a technical distribution, for a sample of size N. I think you might want to check on Extreme Value Distributions. Stating the N is important .... > > e.g. If we are willing to posit that IQ is normally distributed with > mean 100 and sd 15 (there is evidence that this is not the case, but > let's ignore that for this example) and we wanted to estimate the > highest IQ in the USA (let's say the population is 220 million), why > couldn't we repeatedly find the maximum of a sample of 220 million, > distributed this way? > But we never know that a population has a distribution that is *perfectly* normal -- or whatever -- and its precise parameters. Or do we? IQ is a particularly unsettled example (unsettling example?), since IQ is *usually* thought of (plainly mistakenly) as an permanent, personal characteristic. Before WWII, other 'traits' of personal experience, such as racial bigotry, sexism, etc., were imagined as being permanent, in the same way. Conservatively speaking, IQ reports the present ability to score on 'IQ tests'. -- Rich Ulrich, [EMAIL PROTECTED] http://www.pitt.edu/~wpilib/index.html - I need a new job, after March 31. Openings? - . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
