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We revisit the family of goodness-of-fit tests for exponentiality based onthe mean residual life time proposed by Baringhaus & Henze (2008). We motivatethe test statistic by a characterisation of Shanbhag (1970) and provide analternative representation, which leads to simple and short proofs for theknown theory and an easy to access covariance structure of the limitingGaussian process under the null hypothesis. Explicit formulas for theeigenvalues and eigenfunctions of the operator associated with the limitcovariance are derived using results on weighted Brownian bridges. In additionwe provide further asymptotic theory under fixed alternatives and deriveapproximate Bahadur efficiencies, which provide an insight into the choice ofthe tuning parameter with regard to the power performance of the tests.

The test of exponentiality based on the mean residual life function revisited