Isobel did not write the careless paragraph about the central limit theorem (CLT) Don replied to, as pointed out by Digby. I wish to add something to what Don said about the conditions under which the CLT applies, and that people usually miss in considering the universality of the CLT. See below.
>> Let X_1,...., X_n be a sequence of independent, >> identically distributed >> random variables with common mean m and common >> standard deviation >> sigma. Let Z_n be defined as a normalized sum >> >> Z_n = [S_n - m]/ (sigma/sqt root of n), >> S_n = [Z_1 >> +.....+ X_n]/n >> >> S_n is the sample mean >> >> Let F_n(z) be the cumulative probability >> distribution function for Z_n >> and let G(z) be the cumulative probability >> distribution function for the >> standard Normal,. Then F_n(z) --> G(z) as n >> increases. >> >> Note two things about this statement, (1) the >> theorem does not say how >> "fast" the cdf for Z_n approaches the standard >> Normal, (2) the speed of >> convergence depends on z. Also the speed of >> convergence depends on the >> distribution type of the X_i's Note also the sum operation. The CLT, more precisely called the Additive CLT, applies to sums of pairwise independent random variables as n tends to infinity. But if the operation is multiplication with equal-signed r.v., then convergence in distribution is towards the lognormal, not the normal. It might well be that when considering natural phenomena, multiplicative processes be more or equally common than additive ones, as we oftenly observed skewed continuous data. Rubén http://webmail.udec.cl -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and "unsubscribe ai-geostats" followed by "end" on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
