statistics

*To*: mathgroup at smc.vnet.net*Subject*: [mg5835] statistics*From*: Wouter Meeussen Vandemoortele CC R&D <wmn.vdmcc at vandemoortele.be>*Date*: Tue, 28 Jan 1997 03:42:59 -0500*Sender*: owner-wri-mathgroup at wolfram.com

hi, I've never been more than ankle deep into statistics. After reading P. Abbot's item in "In[] and Out[]" of a year ago about expectation values of statistic functions, I wonder if an analytic solution is known for the following old conceptual problem of mine : Make a short list (=sample) of n=4 gaussian random numbers with mu=m and sigma=s, calculate the Mean, Variance, Skewness, Kurtosis and Maximum of this list; Repeat the above procedure many times (10 000 times or so) to get the expected distributions (average & standard deviation) of the Mean, of the Variance, ..etc. Do I end up with normal gaussian distributions ? It can be argued that the Central Theorem implies so. But with what variances in each case ? Repeat the above with n={4,9,16,25,36,49,64,81,100} in order to find the dependence on n, experiment seems to show that: Expected Mean -> m +/- 1.00 s/Sqrt[n] Expected Sqrt(Variance) -> s +/- 0.38 s/Sqrt[n] Expected Skewness -> 0 +/- 2.32 1/Sqrt[n] Expected Kurtosis -> 0 +/- 4.31 1/Sqrt[n] If this assumption is correct (in form), then what are the 0.38, 2.32 and 4.31 analytically? Wouter, NV Vandemoortele Coordination Center Group R&D Center Prins Albertlaan 79 Postbus 40 B-8870 Izegem (Belgium) Tel: +/32/51/33 21 11 Fax:+32/51/33 21 75 vdmcc at vandemoortele.be