Study On Parameter Estimation Method Of Weibull Distribution

The three-parameter Weibull distribution is a more perfect one,and it can describe the probability distribution of the fatigue life of the component equipment more accurately.In this paper,we mainly uses five estimation methods: maximum likelihood estimation,L-moment estimation,percentile method,moment estimation and logarithmic method to estimate the shape parameters?,scale parameters ? and position parameters? of Weibull distribution and compares which method has the best performance.Firstly,the theory of three-parameter Weibull distribution and maximum likelihood estimation is introduced.The maximum likelihood estimation method is used to calculate the estimator of the parameters.Using Newton iterative numerical method and MATLAB programming language,the maximum likelihood estimate value of unknown parameters?,?,? is obtained by using the time data of fatigue life test.Secondly,a new estimation method of L-moment estimation is introduced,and the parameter estimator of Weibull distribution is given according to the relevant definition.The logarithm method,moment estimation method and hund-place method are used to study and discuss the three-parameter Weibull distribution,and their parameter estimators are given respectively.Finally,given sample data,bias and mean square error are used as measurement criteria.The estimated values of the three parameters of Weibull distribution obtained by the five estimation methods are analyzed by taking the sample sizes of 100 and 1000 respectively.According to the graph of deviation and mean square error with sample variation drawn by MATLAB software,it can be concluded that the best performance can be seen from the whole since the likelihood estimation is the best whether the sample size is small or large.The second is the moment estimation method,the percentile method and the moment estimation method,the worst is the logarithmic estimation method overall performance is not ideal.