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doi:10.5194/osd-11-2733-2014
© Author(s) 2014. This work is distributed
under the Creative Commons Attribution 3.0 License.
Research article
08 Dec 2014
Review status
This discussion paper has been under review for the journal Ocean Science (OS). The revised manuscript was not accepted.
A Monte Carlo simulation of multivariate general Pareto distribution and its application
L. Yao1, W. Dongxiao2, Z. Zhenwei3, H. Weihong1, and S. Hui4 1South China Sea Institute of Oceanology, Chinese Academy of Sciences, Guangzhou, China
2State Key Laboratory of Tropical Oceanography, South China Sea Institute of Oceanology, Chinese Academy of Sciences, Guangzhou, China
3School of Civil Engineering and Transportation, South China University of Technology, Guangzhou, China
4China Water Resources Pearl River Planning Surveying & Designing Co., Ltd., Guangzhou, China
Abstract. This paper presents a multivariate general Pareto distribution (MGPD) method and builds a method for solving MGPD through the use of a Monte Carlo simulation for marine environmental extreme-value parameters. The simulation method has proven to be feasible in the analysis of the joint probability of wave height and its concomitant wind from a hydrological station in the South China Sea (SCS). The MGPD is the natural distribution of the multivariate peaks-over-threshold (MPOT) sampling method, and is based on the extreme-value theory. The existing dependence functions can be used in the MGPD, so it may describe more variables which have different dependence relationships. The MGPD method improves the efficiency of the extremes in raw data. For the wave and the concomitant wind from a period of 23 years (1960–1982), the number of the wave and wind selected is averaged to 19 per year. For the joint conditional probability of the MGPD, the relative error is rather small in the Monte Carlo simulation method.

Citation: Yao, L., Dongxiao, W., Zhenwei, Z., Weihong, H., and Hui, S.: A Monte Carlo simulation of multivariate general Pareto distribution and its application, Ocean Sci. Discuss., 11, 2733-2753, doi:10.5194/osd-11-2733-2014, 2014.
L. Yao et al.
L. Yao et al.

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Short summary
MPOT improves the efficiency of the extremes in raw data, and is superior to other methods (the annual maximum). But there are some difficulties (declustering, joint threshold, the resolution method of equation in high dimension) in application of MPOT. The paper shows all processes of analyzing the joint distribution of wind and wave in the South China Sea (SCS), and builds the solving method for MGPD by means of a Monte Carlo simulation.
MPOT improves the efficiency of the extremes in raw data, and is superior to other methods (the...
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