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In this paper we test the composite hypothesis that lifetimes follow anexponential distribution based on observed randomly right censored data.Testing this hypothesis is complicated by the presence of this censoring, dueto the fact that not all lifetimes are observed. To account for thiscomplication, we propose modifications to tests based on the empiricalcharacteristic function and Laplace transform. In the full sample case theseempirical functions can be expressed as integrals with respect to the empiricaldistribution function of the lifetimes. We propose replacing this estimate ofthe distribution function by the Kaplan-Meier estimate. The resulting teststatistics can be expressed in easily calculable forms in terms of summationsof functionals of the observed data. Additionally, a general framework forgoodness-of-fit testing, in the presence of random right censoring, isoutlined. A Monte Carlo study is performed, the results of which indicate thatthe newly modified tests generally outperform the existing tests. A practicalapplication, concerning initial remission times of leukemia patients, isdiscussed along with some concluding remarks and avenues for future research.

Kaplan-Meier based tests for exponentiality in the presence of censoring