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Luis A. Afonso
Posts:
4,699
From:
LIsbon (Portugal)
Registered:
2/16/05


Re: Testing normality by Skewness and Kurtosis: a new focusing
Posted:
Oct 28, 2013 7:46 AM


Skewness and Excess Kurtosis Statistics tests
Setting the Confidence level at 95%, we found the following Confidence Intervals against sizes n, regarding normal (Gaussian) random samples:
______________Skw.______Exc.Kurt.____ __n=20_____+/ 0.742___[1.080, 1.567]__ ____30________0.599___[0.903, 1.223]__ ____40________0.516___[0.802, 1.053]__ ____50________0.453___[0.723, 0.921]__ ____60________0.412___[0.669, 0.830]__ ____70________0.381___[0.626, 0.768]__ ___100________0.313___[0.532, 0.631]__
We aim to compute these interval contents when filled with normal data <CHECK>
__both: Skew and Exc.Kurtosis capture. __whatever: at least one parameter inside __any : no value captured by the intervals.
_____________both___whatever___any_____
__n=20_____0.7710____0.1794___0.0497___Normal ___________0.4264____0.5726___0.0010___Uniform __W= both/(1any)______________________0.811__ _____________________________________ 0.427__ ____30_____0.7439____0.2063___0.0498___ ____40_____0.7293____0.2212___0.0495___ ____50_____0.7107____0.2399___0.0495___ _n=100_____0.6729____0.2775___0.0496___ __W=both/(1any)______Normal___________ 0.708__ _____________________Uniform__________ 0.000_*
* any= 0.000, whatever= 0.9666, any= 0.0334
Conclusion: in the context we are dealing with the test statistics W= both/(1any) is very effective in what concerns to discriminate Uniform to Normal data, even for samples as short as 20. Note: one have 0<= W <=1 these value attained only when any=0, therefore all samples have at least 1 success i.e. fall in one of the two intervals.
Luis A. Afonso



