Testing various classes of life distributions have been considered a very important
problem in the literature during the last decades, and many authors tried to solve it.
In this paper, a new statistic technique for testing exponentiality versus the class of life
distribution used better than aged in increasing concave ordering (UBAC(2)) is introduced
based on the Laplace transform. For this proposed test, the critical values, the
pitman's asymptotic efficiency and the power of the test are calculated via simulation
to assess the performance of the test. A new nonparametric test statistic for testing
exponentiality versus UBAC(2) for right censored data is proposed, and the critical values
are tabulated. Finally, real data are used for complete and censored data by using
our proposed test