Particle Swarm Optimization For Parameter Estimation Of Generalized Extreme Value Distribution

Extreme event(also known as low probability event) that occurs with low probability usually brings severe consequences. As an important branch of modern statistics, extreme value theory provides the theoretical basis for analysis of these rare but severe events. One commonly used probability distribution model in extreme value analysis is generalized extreme value(GEV)distribution that has three key parameters, location, scale and shape.In this thesis, the basic properties and parameter estimation methods of GEV has been firstly reviewed. Specifically, the details of two useful methods, maximum likelihood estimation(MLE)and probability weighted moments(PWMs) are presented. Then, numerical optimization method was proposed to implement the MLE and PWMs for parameter estimation of GEV distribution.The numerical optimization method refers to particle swarm optimization(PSO) in this thesis.As a special case of GEV distribution, parameter estimation of Gumbel distribution has been implemented using MLE combining PSO. But for GEV distribution, PWMs combining PSO was proposed for estimating the shape parameter firstly and then for location and scale parameter,respectively. Numerical experiments show that the newly proposed method can give a reliable estimate of GEV parameters. The efficiency of PSO was verified by the comparison between PSO and two other numerical optimization methods, dichotomization and Newton. The findings and results of this thesis are concluded in the last chapter. Although the newly proposed PWMs plus PSO method does not always outperform other parameter estimation methods, it offers a good and high-efficiency alternative choice.