Parameter Estimation Of Generalized Exponential Distribution Under Censored Life Test

The generalized exponential distribution is a commonly used life distribution.Compared with the gamma distribution and the Weibull distribution,the generalized exponential distribution can better fit the products with skewed data.In order to gain a deeper understanding of the generalized exponential distribution,this paper discusses the parameter estimation problem of the generalized exponential distribution under two bilateral truncated life tests,and applies the method in this paper to a practical example.Firstly,under the two-sided fixed truncated life test,the estimation of shape parammeters of generalized exponential distribution is studied.The maximum likelihood equation of shape parameters is obtained,the existence and uniqueness of the solution of the equation is proved;and when the prior distributions are respectively takes without information prior and conjugate prior,discuss the Bayesian estimation of the shape parameters under the squared loss function and the weighted squared loss function,and it is proved that the estimation is an admissible estimation,and the best linear unbiased estimation of the shape parameters of the generalized exponential distribution is given;next by MATLAB software does random simulation,the results show that Bayesian estimation mation is closer to the truth value of the parameter than the maximum likelihood estimation,and the Bayesian estimation under the squared loss function is better than the Bayesian estimation under the weighted squared loss function,at the same time,when the prior distribution takes the without informative prior distribution,the Bayesian estimation of the shape parameters of the generalized exponential distribution has high accuracy.Secondly,the parameter estimation problem of generalized exponential distribution is studied based on bilateral timed censored life tests.The maximum likelihood estimation of shape parameters is obtained by using the EM algorithm,and the asymptotic variance and approximate confidence interval are given;the expression of the Bayesian estimation estimation under the squared loss function and the weighted squared loss function is obtained under two commonly used prior distributions,prove the admissibility of the estimation;and conduct random simulations,the results show that the simulation effect of Bayesian estimation is better than that of maximum likelihood estimation,and the Bayesian estimation under the squared loss function is batter than the Bayesian estimation under the weighted squared loss function,at the same time,when the prior distribution takes the gamma distribution,the Bayesian estimation of the shape parameters of the generalized exponential distribution is more reliable.Finally,the feasibility of the method used in this paper for two bilateral censored life tests is demonstrated by an example analysis.The results show that the Bayesian estimation is closer to the estimate under the complete data than the maximum likelihood estimation,compared with the Bayesian estimation under the weighted squared loss function,the Bayesian estimation under the squared loss function is more accuracy,in the meantime,the Bayesian estimation that relies on the uninformative prior distribution is more effective under the bilateral fixed censored life tests;the Bayesian estimation under the conjugate prior distribution are more reliable under the bilateral timed censored life tests.