We revisit the family of goodness-of-fit tests for exponentiality based on the mean residual life time proposed by Baringhaus & Henze (2008). We motivate the test statistic by a characterisation of Shanbhag (1970) and provide an alternative representation, which leads to simple and short proofs for the known theory and an easy to access covariance structure of the limiting Gaussian process under the null hypothesis. Explicit formulas for the eigenvalues and eigenfunctions of the operator associated with the limit covariance are derived using results on weighted Brownian bridges. In addition we provide further asymptotic theory under fixed alternatives and derive approximate Bahadur efficiencies, which provide an insight into the choice of the tuning parameter with regard to the power performance of the tests.

翻译：我们根据Baringhaus & Henze(2008年)提出的平均剩余生命时间,重新审视关于指数性的最佳测试体系;我们以Shanbhag(1970年)的特征来激励测试统计,并提供替代表述,从而为已知理论提供简单和简短的证明,便于在无效假设下获取限制高斯进程的共同变量结构;利用加权布朗桥的结果,为与极限常数相关的操作者计算出与极限常数相关的机能和机能的清晰公式;此外,我们还在固定替代品下进一步提供无药可治理论,并得出大约巴哈杜尔效率,从而深入了解关于测试功率的调整参数的选择。