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A family of nonparametric tests is proposed for detecting DMTTF property. The exact distributions of the test statistics are derived under the null hypothesis of exponentiality and critical values are calculated. The proposed test statistics are shown to be asymptotically normal and the consistency of the tests is established. Pitman asymptotic efficacy values are calculated. A large sample test under random censoring is also proposed and the relevant asymptotics are worked out. A Monte Carlo simulation study is carried out in order to assess the merit of the proposed tests. Finally, the test is applied to some real data sets for illustration.

A new family of tests for DMTTF alternatives under complete and censored samples