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

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Luis A. Afonso

Posts: 4,518
From: LIsbon (Portugal)
Registered: 2/16/05
Re: A pertinent/impertinent question. . .
Posted: Nov 5, 2013 4:32 PM
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We will show an alternative algorithm to fit normality based on the separate check of the Skewness and Excess Kurtosis, this time under balanced situation towards the parameters which does not happens at all with the Jarque-Bera test unless sample sizes as large than 4000 and beyond.
We will use as example the size-5o samples.
The test starts by finding the bounds relative the quantiles of S and k:

___Q________S_______k____
__0.99_____0.811____2.201__
__0.98_____0.703____1.769__
__0.97_____0.637____1.518__
__0.96_____0.589____1.349__
__0.95_____0.552____1.220__
__0.94_____0.519____1.117__
__0.93_____0.491____1.030__
__0.92_____0.467____0.954__
__0.91_____0.444____0.888__

And follows by calculating the pair S, k, to which the C.I. reject exactly 0.05 both parameters.
________Both rejected
__0.95_____0.043___
__0.94_____0.051___

At this instance (without prejudice to a further interpolation) we can assure that the intervals [0, 0.52] for S and [0, 1.12] for k, do contain at least one of these estimates in case we are dealing with normal data. Contrarily if the pair relative to the sample problem has both outside the intervals data is very unlikely so.

Luis A. Afonso



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