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Topic: Testing normality by Skewness and Kurtosis: a new focusing
Replies: 1   Last Post: Oct 28, 2013 7:46 AM

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Luis A. Afonso

Posts: 4,615
From: LIsbon (Portugal)
Registered: 2/16/05
Re: Testing normality by Skewness and Kurtosis: a new focusing
Posted: Oct 28, 2013 7:46 AM
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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/(1-any)______________________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/(1-any)______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/(1-any) 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



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