Testing exponentiality has long been an interesting issue in statistical inferences. In this article, we introduce a new measure of distance between two distributions that is similar Kullback–Leibler divergence, but using the distribution function rather than the density function. This new measure is based on the cumulative residual entropy. Based on this new measure, a consistent test statistic for testing the hypothesis of exponentiality against some alternatives is developed. Critical values for various sample sizes determined by means of Monte Carlo simulations are presented for the test statistics. Also, by means of Monte Carlo simulations, the power of the proposed test under various alternative is compared with that of other tests. Finally, we found that the power differences between the proposed test and other tests are not remarkable. The use of the proposed test is shown in an illustrative example.

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