I found a new estimator for tail index in GEV distribution (GEV.ALPHA).

I generate 1000 alpha stable random variables (with a=1 , a=0.5 , a=2 seperately) and repeat it 1000 times (in matlab).

then I used  GEV.ALPHA estimator to estimate the tail index in alpha stable distribution.

The results were excellent and the MSE was quite small.

Any one know why??

Can we estimate the tail index  of stable distribution with an estimator which is based on GEV distribution??