Abstract
We propose an estimator of the survival function of a random variable which is constructed through the Total Time on Test (TTT) when the data are randomly right censored. The new method is motivated by the maximum likelihood method for estimation of monotone failure rates and it bears a close resemblance to the classical estimator by Nelson (1969). It is shown that the asymptotic properties of the new estimator are the same as those of the Nelson estimator and the Kaplan-Meier (K-M) estimator, and that this estimator has a smaller MSE for small and moderate sample sizes. Specifically, for data that are heavily censored, we show through a simulation study that the proposed estimator has a sipficantly smaller MSE, compared with both the Nelson and K-Mind estimators, almost uniformly over the support of the underlying distribution.
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