Estimation and Goodness-of-Fit in the Case of Randomly Censored Lifetime Data

A new continuous distribution function estimator for randomly censored data is developed, discussed, and compared to existing estimators. Minimum distance estimation is shown to be effective in estimating Weibull location parameters when random censoring is present. A method of estimating all 3 parameters of the 3-parameter Weibull distribution using a combination of minimum distance and maximum likelihood is also given. Cramer-von Mises and Anderson-Darling goodness-of-fit test statistics are modified to measure the discrepancy between the maximum likelihood estimate and the Kaplan-Meier product-limit estimate of the distribution function of the random variable of interest. These modified test statistics are used to construct goodness-of-fit tests for the exponential, Weibull (shape 2), and Weibull (shape 3.5) distributions when the censoring distribution is assumed to be exponential. Percentage points are obtained via Monte Carlo simulation. More generally, elements of competing risks theory are used to build goodness-of-fit tests using crude lifetimes. For tests based on crude lifetimes, the assumption of an exponentially distributed censoring variable and special estimation techniques are no longer required. Further, complete sample goodness-of-fit techniques may be used, bringing much more flexibility to goodness-of-fit testing when samples are randomly right-censored