Inferences on Parametric Estimation of Distribution Tails
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We propose a general method for parameter estimation of a distribution tail that does not depend on the fulfillment of the conditions of the Gnedenko theorem. We prove the consistency of the proposed estimator and its asymptotic normality under stronger conditions imposed on the parametric family of distribution tails. Additionally, the proposed method is adapted for estimating the Weibull and log-Weibull tail indices.
This work was supported by the Russian Science Foundation, project no. 19-11-00290.