Extreme value prediction with modified Enhanced Monte Carlo method based on tail index correction

Abstract

As one of the main branches of extreme statistics, extreme value theory is widely used in marine engineering. Due to its special application in real ocean environmental states, the scale of the obtained monitoring data is limited. Aiming at the problem of extreme value prediction of different return periods with medium-scale data, this paper proposes a modified Enhanced Monte Carlo (EMC) extreme value prediction method based on the tail index correction. First, the Hill-type estimator is introduced to quantitatively evaluate the tail behavior of the data. Tail behavior analysis is then performed for sample data of various typical distribution functions, and a modified EMC method based on the tail index is proposed. Furthermore, tail estimator extrapolation is performed for a situation where the estimator does not converge to improve the engineering applicability of the proposed method. Based on a series of numerical and engineering examples, the extreme value prediction performance of the proposed method is compared with the classical extreme value prediction methods. The results show that the modified EMC extreme value prediction method proposed in this paper can provide useful guidance for the extreme value analysis of marine environmental loads and structural responses. At the same time, the method proposed in this paper introduces the slow-varying assumption in the classical EMC method, and the limitations caused by the assumption are also discussed.