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Successful application of extreme value statistics for estimating the Pareto tail index relies heavily on the choice of the number of extreme values taken into account. It is shown that these tail index estimators can be considered estimates of the slope at the right upper tail of a Pareto quantile plot, obtained using a weighted least squares algorithm. From this viewpoint, based on classical ideas on regression diagnostics, algorithms can be constructed searching for that order statistic to the right of which one obtains an optimal linear fit of the quantile plot.

A general class of estimators of the extreme-value index is generated using estimates of mean, medium and trimmed excess functions. Special cases yield earlier proposals in the literature, such as Pickands' (1975) estimator. A particular restatement of the mean excess function yields an estimator which can be derived from the slope at the right upper tail from a generalized quantile plot. From this viewpoint algorithms can be constructed to search for the number of extremes needed to minimize the mean square error of the estimator. Basic asymptotic properties of this estimator are derived. The method is applied in case studies of size distributions for alluvial diamonds and of wind speeds.

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