The usage of the largest observations for parameter and quantile estimation for the Gumbel distribution; an efficiency analysis
Résumé
We analyze the efficiency of the method proposed by I. Weissman for the estimation of the parameters and quantiles for the Gumbel distribution. We compare Weissman's method which uses the k largest observations, with the known (Gumbel) method and prove that essentially, Gumbel's method is more efficient than Weissman's method. This comparison is based on the Cramer-efficiency and on the efficiency with respect to the quantile estimation.
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