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Topic: Normal parameters not explicit
Replies: 0

 Luis A. Afonso Posts: 4,758 From: LIsbon (Portugal) Registered: 2/16/05
Normal parameters not explicit
Posted: Dec 12, 2013 12:41 PM

Normal parameters inexplicit

People may be puzzled why test statistics on normal data, like Jarque-Bera´s, central moments,does not explicit the Population parameters, mu and sigma.

Here is a test statistics mean value record I obtained for different sample sizes:

___Skew____Kurt_______mu__sigma___
__n=50
___0.088___29.935______14____8___
___0.026___29.983______99___10___
___0.031___30.032______40___11___
__n=100
__-0.090___60.222______51___16___
__-0.041___59.942______49____5___
__-0.144___60.233______48___12___
__n=200
__-0.031__119.784______15____9___
__ 0.065__ 119.642______99__ 17___
__ 0.120__ 119.801______19__ 15___
__n=500
__ 0.124__ 300.696______86__ 18___
__ 0.120__ 301.071______67___ 6___
__-0.018__ 299.755______25__ 15___

The results are eloquent: either the mean or the Population standard deviation do have any influence regarding S and K in spite of they were obtained randomly: Skew both sides of 0, Kurtosis about 30.60,120, 300.

Reason?
If we consider the Skew we see that m3/(m2^1.5) the numerator and denominator *mark* 3 points because 2x1.5=3.The same for Kurtosis: m4/(m2^2), these time 4 points.

Luis A. Afonso