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Point Estimation of the Parameter of a Truncated Exponential Distribution

This paper addresses point estimation of the failure rate parameter for a 1-parameter exponential distribution, based on random samples taken from a severely right-truncated distribution (truncation point known). The maximum likelihood estimation (MLE) leads to frequent estimates of zero failure rate, even for large samples. We suggest two alternative estimators which overcome this problem, a Bayes estimator and a composite estimator. These estimators are compared, through Monte Carlo trials, with the MLE, both in terms of s-bias and root mean square (rms) error. Based on these comparisons, the composite estimator is recommended. A numerical example illustrates the use of these estimators.