We extend Hill's well-known estimator for the index of a distribution function with regularly varying tail to an estimate for the index of an extreme-value distribution. Consistency and asymptotic normality are proved. The estimator is used for high quantile and endpoint estimation.
"A Moment Estimator for the Index of an Extreme-Value Distribution." Ann. Statist. 17 (4) 1833 - 1855, December, 1989. https://doi.org/10.1214/aos/1176347397