A test of exponentiality versus alternatives containing the RNBUE class derived from the Laplace empirical transform

A scale–free test for exponentiality is proposed which is consistent within an extended set of models which includes, but is not limited to, the ‘renewal new better than used in expectation’ (RNBUE) class of life distributions. The limiting null distribution of the test statistics is derived, and the approximate local Bahadur efficiency is calculated for several families of alternatives. The finite–sample properties of the proposed procedures are investigated via simulation.