Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.stat.math.independent

Topic: A pertinent/impertinent question. . .
Replies: 8   Last Post: Nov 13, 2013 4:02 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ] Topics: [ Previous | Next ]
Luis A. Afonso

Posts: 4,615
From: LIsbon (Portugal)
Registered: 2/16/05
Re: A pertinent/impertinent question. . .
Posted: Nov 4, 2013 12:59 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Repeating

Skewness and Excess Kurtosis Statistics tests

Once showing that JB test is unsuitable to treat short samples we try another way.

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_*

* both= 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



Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.