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:
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.