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We use bias-reduced estimators of high quantiles, of heavy-taileddistributions, to introduce a new estimator of the mean in the case of infinitesecond moment. The asymptotic normality of the proposed estimator isestablished and checked, in a simulation study, by four of the most populargoodness-of-fit tests for different sample sizes. Moreover, we compare, interms of bias and mean squared error, our estimator with Peng's estimator(Peng, 2001) and we evaluate the accuracy of some resulting confidenceintervals.

A Bias-reduced Estimator for the Mean of a Heavy-tailed Distribution with an Infinite Second Moment