A tail estimator for the index of the stable paretian distribution∗
- 1 January 1998
- journal article
- research article
- Published by Taylor & Francis in Communications in Statistics - Theory and Methods
- Vol. 27 (5) , 1239-1262
- https://doi.org/10.1080/03610929808832156
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.Keywords
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