Timeline for what is the meaning of 'tail' of kurtosis?
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| Nov 20, 2017 at 0:27 | comment | added | BigBendRegion | Also, the given "definition" of heavier-tailed is actually quite silly. By that definition, the N(0,1) distribution is heavier-tailed than the .9999*U(-1,1) + .0001*U(-1000,1000) distribution. The latter distribution is extremely outlier-prone and has very high kurtosis, the former is not outlier-prone at all and has low kurtosis. The argument is a complete red herring, because it is not even a logical measure of "tailedness". | |
| Nov 9, 2017 at 13:19 | comment | added | BigBendRegion | There is not just one measure of tails. E{Z^4*I(|Z| >1)} is one, E{Z^10 *I(|Z| > 5} another. For a sequence of distributions where kurtosis tends to infinity, E{Z^4 *I(|Z| > b)}/kurtosis -> 1, for any b; hence, large kurtosis is mostly determined by the tail. Further, the contribution of |Z| <1 to kurtosis is small, as noted below, for all distributions. Hence, kurtosis itself is a measure of tailweight, although not identical to other tailweight measures. Similarly, other tailweight measures do not measure the same thing as kurtosis. There are, after all, infinitely many tailweight measures. | |
| Apr 13, 2017 at 12:44 | history | edited | CommunityBot |
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| Sep 15, 2015 at 2:26 | history | edited | Glen_b | CC BY-SA 3.0 |
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| Sep 15, 2015 at 2:15 | history | edited | Glen_b | CC BY-SA 3.0 |
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| Sep 15, 2015 at 1:01 | history | answered | Glen_b | CC BY-SA 3.0 |