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In this paper we continue the investigation of the SRCEN estimator of theextreme value index $\gamma$ (or the tail index $\alpha=1/\gamma$) proposed in\cite{MCE} for $\gamma>1/2$. We propose a new estimator based on the localmaximum. This, in fact, is a modification of the SRCEN estimator to the case$\gamma>0$. We establish the consistency and asymptotic normality of the newlyproposed estimator for i.i.d. data. Also, a short discussion on the comparisonof the estimators is included.

Modification of Moment-Based Tail Index Estimator: Sums versus Maxima