A Likelihood Ratio Statistic for Testing Goodness of Fit with Randomly Censored Data

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Abstract
A likelihood ratio statistic is proposed for testing goodness of fit with grouped data which are subject to random right censoring. Under appropriate conditions, this statistic has an asymptotic chi-square distribution which is non-central under contiguous alternatives. A formula is given for the non-centrality parameter. An example concerns data from a large scale animal survival study with serial sacrifice where it is attempted to fit the Weibull, Gompertz and exponential power distributions to life length. Another example concerns human marihuana usage and this needs an extension of the test to the doubly censored case. Another use of the statistic is to provide a quantitative method of ranking the fit of various proposed models to survival or reliability data.