       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

```

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