Method Of Estimation For 2-parameter Weibull Distribution Based On Truncated And Censored Data

Weibull distribution is a kind of life distributions and has wide applications in the field of reliability.In life analysis,the data may be incomplete for various reasons.The left truncation and right censored data is a common type of incomplete data.This thesis studies estimating parameters of 2-parameter Weibull distribution under the left truncated and right censored data.In the existing studies,the methods of estimation are mainly Newton's method and expectation maximization algorithm.However,when the number of truncated data is large and the sample size is small,these methods depend on the choice of initial value.And the most important deficiency is the accuracy of parameters which need to be further improved.Because the more accurate parameters are,the more efficient 2-parameter Weibull distribution will be.As Newton downhill method can broaden the selection of the initial value range,this thesis proposes a new method,parameter two-step iterative method,to estimate the parameters.This new method first uses Newton downhill method to solve the problem of parameter estimation of 2-parameter Weibull distribution in the left truncated right censored data.Therefore the new method weakens the dependence on the initial value.Based on this step,using the estimation of the shape parameter,the new method can improve estimation's accuracy of the scale parameter.The aim of improving the overall estimation's accuracy of two parameters of Weibull distribution is obtained in the case of small sample and high truncation ratio.Finally,this thesis applies the new method to two real data sets and one simulated data set.The numerical results show that the estimation of the new method is better than the other methods.