Parameter estimation of linear exponential distribution under type-II doubly censored sample

The maximum likelihood estimation and Bayes estimation of unknown parameters in linear exponential distribution are discussed under the type-II doubly censored sample. The maximum likelihood estimation of unknown parameter is obtained by Newton-Raphson iterative method, and the unique existence of maximum likelihood estimation is proved. The Bayes approximate estimates of the parameters are discussed by Tierney-Kadane approximation under symmetric loss function and asymmetric loss function by selecting non-informative prior distribution and conjugate prior distribution. The mean square error of maximum likelihood estimation and Bayes estimation of unknown parameters is simulated by MatlabR200b. The results show that the mean square error of Bayes estimation of unknown parameters is the smallest when the Gamma prior distribution is selected and the squared loss function is used under different sample sizes and different censored schemes.