  In this paper we test the composite hypothesis that lifetimes follow an
exponential distribution based on observed randomly right censored data.
Testing this hypothesis is complicated by the presence of this censoring, due
to the fact that not all lifetimes are observed. To account for this
complication, we propose modifications to tests based on the empirical
characteristic function and Laplace transform. In the full sample case these
empirical functions can be expressed as integrals with respect to the empirical
distribution function of the lifetimes. We propose replacing this estimate of
the distribution function by the Kaplan-Meier estimate. The resulting test
statistics can be expressed in easily calculable forms in terms of summations
of functionals of the observed data. Additionally, a general framework for
goodness-of-fit testing, in the presence of random right censoring, is
outlined. A Monte Carlo study is performed, the results of which indicate that
the newly modified tests generally outperform the existing tests. A practical
application, concerning initial remission times of leukemia patients, is
discussed along with some concluding remarks and avenues for future research.
