Parameter Estimation For Lindley Distribution Based On Censored Data

In 1958,Lindley first proposed the Lindley distribution,which was mainly used to analyze life data.Today,many scholars have extended the research on this distribution and achieved certain research results.Given that the Lindley distribution has better adaptability and flexibility than the exponential distribution,it is necessary to study the relevant statistical properties of the Lindley distribution.At the same time,censored data often appears in life test and reliability analysis,attracting many scholars to participate in research,and then promote the continuous development and improvement of the basic theory of censored data.This paper will mainly study the parameter estimation of Lindley distribution under progressive Type-? interval censored data and progressive Type-? hybrid censored data.The specific research content is divided into the following five parts.The first part,mainly introduces the Lindley distribution,expounds the research status of Lindley distribution at home and abroad,and combines the historical research background to analyze its theoretical value and research significance in the case of censored data.In the second part,the parameter estimation of the Lindley distribution is discussed mainly under the progressive Type-? interval censored data.In order to obtain the parameter estimation value,the Newton-Raphson iterative method is used to solve the approximate solution of the maximum likelihood estimation of Lindley distribution parameters.At the same time,the maximum likelihood estimation of the Lindley distribution reliable function and the risk function is obtained.Finally,the validity of the Lindley distribution is verified by numerical simulation.In the third part,the Bayesian estimation of the Lindley distribution parameters under the square loss function and the entropy loss function are discussed under the progressive Type-? interval censored data.In order to simplify the calculation process,the estimator is calculated by Lindley approximation method.At the same time,the Bayesian estimation of the reliable function and risk function of Lindley distribution based on the squared loss function is obtained.and the mean and mean square error of Bayesian estimation under the two loss functions are calculated by numerical simulation.Finally,the mean and mean square error of the Bayesian estimation andthe Bayesian estimation of the reliability function and the risk function are calculated by numerical simulation,and compared with the maximum likelihood estimation.In the fourth part,the parameter estimation problem of Lindley distribution is discussed mainly under the progressive Type-? hybrid censored data.In order to improve the accuracy of the estimated value and make the estimated value more stable,the EM algorithm is used to calculate the maximum likelihood estimation of the Lindley distribution parameters,and the numerical simulation is used to test.In the fifth part,the Bayesian estimation of Lindley distribution parameters under the square loss function and the entropy loss function are discussed under the progressive Type-? hybrid censored data.The numerical solution of Bayesian estimation is obtained by Lindley approximation method,and the mean and mean square error of Bayesian estimation under the two loss functions are calculated by numerical simulation,and compared with the maximum likelihood estimation obtained by EM algorithm.