Estimation methods for the mean of the exponential distribution based on grouped and censored data

For grouped and censored data from an exponential distribution, the method of maximum likelihood (ML) does not in general yield a closed-form estimate of the mean, and therefore, an iterative procedure must be used. Considered are three approximate estimators of the mean: two approximate ML estimators and the midpoint estimator. Their performances are compared by Monte Carlo simulation to those of the ML estimator, in terms of the mean square error and bias. The two approximate ML estimators are reasonable substitutes for the ML estimator, unless the probability of censoring and the number of inspections are small. The effect of inspection schemes on the relative performances of the three approximate methods is investigated