In article <[EMAIL PROTECTED]>, Duke of Hazard <[EMAIL PROTECTED]> wrote: >I have two questions on the following statement taken from an intro. >stats textbook:
>"It can be shown under very general assumptions that the distribution >of independent random errors of observation takes on a normal >distribution as the number of observations becomes large." The author(s) of that textbook do not understand what they are saying. The simplest form of the Central Limit Theorem is that the distribution of the sum of independent random variables with a common distribution with a finite variance approaches a normal distribution. The rate of approach is not that fast. The theorem generalizes. >1) What are these "general assumptions"? Is it based on probability of >deviation from a mean being proportional to the deviation divided by >the mean? I suggest you study a good probability book. The above is only true for the uniform distribution. >2) Given these assumptions, how can one derive the mathematical >equation for the normal distribution curve? De Moivre derived it around 1731 by using Stirling's formula (asymptotic) for factorials and passing to the limit. The normal was originally derived as an approximation to the binomial with large variance. -- 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/ . =================================================================
