Hi Sachin Date,
I’m not sure I understand why there is a lower bound on the acceptance region for the JB statistic. I’ve read up a bit on the chi squared distribution, skewness, kurtosis etc and find that when I generate histograms representing Gaussian distributions I often get JB < .05. To me this is good, because it circumscribes the skew and excess kurtosis to an ellipse quite close to (0, 0).
Why am I delving into all this? First because I am uncomfortable blindly using tests without some degree of understanding/confidence of the math or its interpretation. Second, very practically, I am trying to distinguish a Laplace from a Gaussian distribution.
Most DS fail to look at the histograms on a semi-log plot, neither are they looking for the cusp: people had been staring at the orange distribution for months and it took only “one click” to see that it was not Gaussian but Laplace.
Of course, when you regress them it is clear what is going on:
For smaller populations, with more noise and the “outlier sensitivity” of the higher moments, I need a good test to distinguish the two. Aside from the obvious problems due to the long-tailed ness, the mechanisms, the physics or the phenomenology behind the two are very different.
I welcome any thoughts or suggestions email@example.com