Estimation of the conditional tail moment for Weibull-type distributions

We consider the estimation of the conditional tail moment at extreme levels for the class of Weibull-type distributions. A two-step procedure is introduced where in the first stage one estimates the conditional tail moment at an intermediate level, followed by an extrapolation in the second stage. The asymptotic properties of the estimators introduced in the two stages are derived under suitable assumptions. The finite sample properties of the proposed estimator are examined with a simulation experiment. We conclude with two applications on real life data: wind speed measurements collected at an offshore wind farm and (Formula presented.) air pollution data.