This is my qq plot : enter image description here

Its concave-convex curve so it indicates light tails. But my mean excess plot :

enter image description here

is increases which means the tail of the distribution of my data is heavy-tailed.

I don't understand why. Some help would be appreciated.

  • $\begingroup$ Why do you have such huge white space around your plots? I can't read your axes $\endgroup$ – Glen_b Jun 17 '18 at 0:07
  • $\begingroup$ I used the mean excess function in R. in y-axis : The mean excess values and in x-axis : the threshold. $\endgroup$ – user44677 Jun 17 '18 at 0:10
  • $\begingroup$ I have posted versions of your plots with the excess white space removed. You may still need to add additional information to make what you did sufficiently clear. $\endgroup$ – Glen_b Jun 17 '18 at 0:12
  • $\begingroup$ Someone can explain me why are the data points clustering in the mean excess plot and in the QQ-plot too ? thanks in advance $\endgroup$ – user44677 Jun 17 '18 at 1:29
  • 1
    $\begingroup$ Those are examples of things that would give a hard cut off (either by truncation or winsorization) where otherwise the amount recorded may be larger. $\endgroup$ – Glen_b Jun 19 '18 at 9:09

One can define the mean-excess function to be:

$$e_X(d) = \mathbb E(X - d | X > d )$$

If a distribution has a thin tail, I'd expect this function to get smaller and smaller if I keep increasing $d$. That's exactly what's happening with your function over the threshold $X = 2e+06$.

The ME plot is meant to be interpret after a particular threshold (because you're only interested in the tail of this distribution).

  • $\begingroup$ So should I use GPD or GEV distribution ? What about the QQplot? thanks in advance $\endgroup$ – user44677 Jun 17 '18 at 15:47

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