pseudo likelihood function

Suppose that the lifetime distribution of a random sample of n experimental units is exponential with hazard rate θ and due to time constraints and cost reduction, interval censoring data schemes is used by the experimenter. In this research, some of the existing parameter estimators of the exponential lifetimes under interval censoring are considered. In addition, three new weighted estimators are introduced. we compare the performance of our three methods with some of the existing parameter estimators through simulation studies. For a given sample size n and k inspection times, t1, t2, . . . , tk from the exponential distribution and for each scenario, bias and mean of square error (MSE) are calculated. In addition, the relative efficiency of the proposed estimators are taken into consideration. Moreover, based on the simulation study, their performances are compared to the existing methods. Finally, the asymptotic distribution of one investigated method, which has the best performance, is obtained.