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.

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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.

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Of course, when you regress them it is clear what is going on:

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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 isaranjeet@gmail.com

Thanks, Ranjeet

I stop to miau to cats.

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