  Estimating the tail index parameter is one of the primal objectives in
extreme value theory. For heavy-tailed distributions the Hill estimator is the
most popular way to estimate the tail index parameter. Improving the Hill
estimator was aimed by recent works with different methods, for example by
using bootstrap, or Kolmogorov-Smirnov metric. These methods are asymptotically
consistent, but for tail index $\xi >1$ and smaller sample sizes the estimation
fails to approach the theoretical value for realistic sample sizes. In this
paper, we introduce a new empirical method, which can estimate high tail index
parameters well and might also be useful for relatively small sample sizes.
