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In this paper, we study the existence and consistency of the maximum likelihood estimator of the extreme value index based on - record values. Following the method used by Drees et al. (2004) and Zhou (2009), we prove that the likelihood equations, in terms of - record values, eventually admit a strongly consistent solution without any restriction on the extreme value index, which is not the case in the aforementioned studies.

journal of probability and statistics

On the Maximum Likelihood Estimation of Extreme Value Index Based on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>k</mml:mi></mml:math>-Record Values

On the Maximum Likelihood Estimation of Extreme Value Index Based on k-Record Values