A tail estimator for the index of the stable paretian distribution

Abstract

A new tail estimator for the index α of stable Paretian distributions is considered. The problem of specifying integer k$_{1}$ which determines the tail area used for estimation, is investigated for all three estimators, and shown that the optimal k value for the new estimator is highly insensitive to the true value of index α. As a result, in contrast to existing tail estimators such as the widely used Hill estimator, a simple rule for choosing k can be established. Finally, the small sample properties of the new estimator are examined.