Bayesian Estimation For The Parameter Of Lindley Distribution

The Lindley distribution was first proposed by the British statistician Lindley,which plays a very prominent role in life test and reliability analysis.Nowadays,some achievements have been made in the research of Lindley distribution.Censored data and progressive Type-? interval censored data often appear in life test and reliability analysis.In recent years,statisticians have studied and solved many problems around these data samples.Bayes theory is an important part of statistical decision theory,which has been studied and applied by more and more statistical workers in various fields of statistics.In this paper,we will study the parameter estimation of Lindley distribution under censored data and progressive Type-?interval censored data and study the problem of the following aspects:Firstly,the historical background and significance of this research,the main research work at home and abroad,as well as the main work and theoretical basis of this research are introduced and elaborated.Secondly,based on complete data,the parameter estimation problem of Lindley distribution was studied and the bayesian estimation expressions of parameters under square loss function,MLINEX loss function and compound MLINEX symmetric loss function,were obtained.The numerical simulation results by R software showed that the accuracy of bayesian estimation increased with the increase of sample size.Then,the parameter estimation problem of Lindley distribution is studied under censored data model.The iteration formula of the parameter maximum likelihood is obtained,based on square loss function,MLINEX loss function and compound MLINEX symmetric loss function,the expression of parameter bayesian estimation is obtained,and the numerical simulation is done by R software.The simulation shows that both methods are suitable for parameter estimation under censored data.However,in the case of bayesian estimation,the accuracy of the estimate obtained by using the square loss function is higher than that obtained by using the other two loss functions.Finally,under progressive Type-? interval censored data,the estimation of Lindley distribution parameters was studied.The iteration of maximum likelihood estimation was obtained and the bayesian estimation based on square loss function,MLINEX loss function and compound MLINEX symmetric loss function,was obtained respectively.But the bayesian estimation cannot be directly calculated results,using Lindley approximation method to get the approximate solution of bayesian estimation.Numerical simulation was carried out by R software.The results show that both estimation methods are applicable to the parameter estimation of Lindley distribution under progressive interval censored data.The accuracy of bayesian estimation increases with the increase of sample size,and the Bayesian estimation which depends on the square loss function is closer to the true value.And we also found that if we change the observation time to estimate the parameters,the maximum likelihood and Bayes estimates are less affected.The method of this paper is demonstrated by examples.The results show that the bayesian estimation of the parameters in the square loss function is the closest to the maximum likelihood estimation under complete data and censored data.The value of maximum likelihood estimation is greater than that of complete data,and the value of bayesian estimation is less than that of complete data under progressive type-? interval censored data.