Luis A. Afonso
Posts:
4,758
From:
LIsbon (Portugal)
Registered:
2/16/05


Re: A pertinent/impertinent question. . .
Posted:
Nov 5, 2013 4:32 PM


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 JarqueBera test unless sample sizes as large than 4000 and beyond. We will use as example the size5o 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

