Abstract
Maximum likelihood estimation method is used to solve the problem of parameter estimation of three-parameter generalized extreme value distribution. Based on the theory of order reducing，a new numerical algorithm is presented to resolve the problem of maximum likelihood estimation of three-parameter generalized extreme value distribution．Firstly，the shape parameter is assumed to be known and ternary likelihood equations can be transferred into binary ones that are solved with the dichotomy．And then，scale and location parameters are the functions of shape parameter. Further，the maximum likelihood function is described as a unitary function of shape parameter. The optimal estimation of shape parameters can be obtained by applying dichotomy again.
Highlights
Wind disaster is one of the most serious natural disasters in the world
Limited to the current technical level, the research of this method can not be used in practice; the second method is called annual maximum wind action time series method, which is suitable for structural design with less obvious aeroelastic effect; the third method is based on the joint distribution of wind speed and direction [2]
We should collect and use more abundant and accurate original data of wind speed; on the other hand, we should improve the accuracy of statistical methods
Summary
Wind disaster is one of the most serious natural disasters in the world. In order to effectively avoid wind disaster, the determination of wind load plays an important role in building structure design. A new numerical method is proposed for the maximum likelihood equations of three parameter extreme wind speed distribution parameters by combining the order reduction method with the dichotomy method This method doesn't need to give initial value, and it's simple and fast, and it's not limited by the number of samples. Based on the wind speed data of Baoshan meteorological station in Shanghai, this paper discusses the solution strategy of the nonlinear equation of extreme value distribution by combining with the maximum likelihood method, and establishes an efficient and strong stability analysis method step by step iterative estimation method. This method uses the probability weighted moment of the sample to estimate the probability weighted value of the population to obtain the parameter estimation [22]
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