In article <[EMAIL PROTECTED]>, Donald Burrill <[EMAIL PROTECTED]> wrote: >(Reply to Peter and to the edstat list.)
>"But given a finite population...": > Yes, well, that's exactly the question, isn't it? If the population is >normal, it isn't finite; if it's finite, it isn't normal, except >approximately, in some (usually ill-defined) sense of "approximately". >Seems to me Peter's examples are not of a "finite normal population" >(which seems to me an oxymoron), but of a way of approaching the >expected value of the maximum of a rather large sample (assumed to be) >drawn from a normal population. >It is not that this is unreasonable; it's just that it's not how the >original question was put. (Now, it might be closer to what the >original question was _intended_ to be; but I have no way of assessing >that, in the absence of a telepathic connection to Howard Kaplon's >colleague's student.) >I seem to recall having read, years ago, of something called "extreme >value theory". Presumably it would have application here... > -- Don. This is correct, given the parameters. Given the values observed, with the parameters to be estimated, it is somewhat harder. One should probably use extreme value theory on the unobserved part of the finite population, in full knowledge of how large it is, and what the form of the distribution is. Without this, even given the size of the population, one can only estimate reasonably the position of the largest sample element in the population. The tail of a distribution cannot be well estimated from the "body" without making strong assumptions. >On Mon, 22 Mar 2004, Peter Flom wrote in part: >> Clearly ... 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....) -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University [EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558 . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
