A new method for estimating the tail index using truncated sample sequence

09/11/2022

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by   F. Q. Tang, et al.

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This article proposes a new method of truncated estimation to estimate the tail index α of the extremely heavy-tailed distribution with infinite mean or variance. We not only present two truncated estimators α̂ and α̂^' for estimating α (0<α≤ 1) and α (1<α≤ 2) respectively, but also prove their asymptotic statistical properties. The numerical simulation results comparing the six known estimators in estimating error, the Type I Error and the power of estimator show that the performance of the two new truncated estimators is quite good on the whole.