This is my qq plot :

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

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.

• Why do you have such huge white space around your plots? I can't read your axes – Glen_b Jun 17 '18 at 0:07
• I used the mean excess function in R. in y-axis : The mean excess values and in x-axis : the threshold. – user44677 Jun 17 '18 at 0:10
• 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. – Glen_b Jun 17 '18 at 0:12
• Someone can explain me why are the data points clustering in the mean excess plot and in the QQ-plot too ? thanks in advance – user44677 Jun 17 '18 at 1:29
• 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. – Glen_b Jun 19 '18 at 9:09

$$e_X(d) = \mathbb E(X - d | X > d )$$
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 $X = 2e+06$.