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Atallah et al. [10] and Al-Gashgari et al. [9] achieved a new technique for testing exponentiality based on Laplace transform, in this paper we introduce a new test for testing exponentiality versus ”exponential better than used in moment generating function ordering class”(EBUmgf ). By simulation, the critical values and the powers of the proposed test under various alternatives are calculated to assess the performance of the test. It is shown that the proposed test enjoys good power and performs better than some previous tests in terms of Pitman’s asymptotic efficiencies for several alternative. Finally sets of real data are used as examples to illustrate the use of the proposed test in practical application.

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