A Least-Squares Fitting Method for Generalized Pareto Distributions Based on Quantiles

ZHAO Gang; LI Gang

doi:10.21656/1000-0887.380196

Volume 39 Issue 4

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ZHAO Gang, LI Gang. A Least-Squares Fitting Method for Generalized Pareto Distributions Based on Quantiles[J]. Applied Mathematics and Mechanics, 2018, 39(4): 415-423. doi: 10.21656/1000-0887.380196

Citation:

ZHAO Gang, LI Gang. A Least-Squares Fitting Method for Generalized Pareto Distributions Based on Quantiles[J]. Applied Mathematics and Mechanics, 2018, 39(4): 415-423. doi: 10.21656/1000-0887.380196

Citation:

ZHAO Gang, LI Gang. A Least-Squares Fitting Method for Generalized Pareto Distributions Based on Quantiles[J]. Applied Mathematics and Mechanics, 2018, 39(4): 415-423. doi: 10.21656/1000-0887.380196

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A Least-Squares Fitting Method for Generalized Pareto Distributions Based on Quantiles

doi: 10.21656/1000-0887.380196

ZHAO Gang,
LI Gang

State Key Laboratory of Structural Analysis for Industrial Equipment(Dalian University of Technology);Department of Engineering Mechanics, Dalian University of Technology, Dalian, Liaoning 116024, P.R.China

Funds: The National Basic Research Program of China(973 Program)（2016CB046506）

Received Date: 2017-07-14
Rev Recd Date: 2018-01-09
Publish Date: 2018-04-15

Abstract

Abstract

The generalized Pareto distribution (GPD) is a classical asymptotically motivated model for excesses above a high threshold based on the extreme value theory, which is useful for the high reliability index estimation. In the GPD there are 2 unknown parameters which could be estimated with the least-squares fitting method and the maximum likelihood method. Both methods need all the tail samples of a distribution in previous studies. However, for the GPD estimation, the better accuracy would lead to a much higher computational cost. So a least-squares fitting method based on the quantiles was proposed to obtain the unknown parameters in the GPD. The 2-stage-updating method for the Kriging model was also given to calculate the quantiles. Compared with the GPD based on the maximum likelihood method and the Monte-Carlo method, the 2-stage-updating method for the Kriging model helps find the specified quantiles accurately and efficiently, and the least-squares fitting method based on the quantiles also performs well.
- generalized Pareto distribution,
- least-squares fitting method,
- quantile,
- Kriging model

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References(17)

References

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