In article <[EMAIL PROTECTED]>, Andrew Morse <[EMAIL PROTECTED]> wrote:
>Three questions, in increasing order of generality... > 1. Does a general method exist for calculating the expected >standard deviation of N samples taken from an arbitrary, known >probability distribution? Do you mean samples of size N? And do you mean the sample standard deviation, or what? However, the answer is very likely to be no; square roots mess things up. > 2. Does a general method exist for calculating the expected >distribution of standard deviations of repeated trials of N samples >taken from an arbitrary, known probability distribution? This can only be done in closed form for a few distributions. This even applies to the simpler problem of the second moment about 0. Using complex variable methods, it may well be possible to do it numerically in a reasonable amount of time. The general method for this, if it can be done, is to compute the characteristic function of the moment, raise it to the N-th power, and invert. > 3. Does a general method exist for calculating the expected >distribution of any of the moments of repeated trials of N samples taken >from an arbitrary, known probability distribution? The same remarks as above hold. If the 2k-th moment exists, the Central Limit Theorem gives the asymptotic normal distribution of the k-th moment about 0. Similar results hold for ths standard deviation of th fourth moment exists. These asymptotic results are very old. -- 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/ . =================================================================
