Testing Goodness-of-Fit for Exponential Distribution Based on Cumulative Residual Entropy

Abstract

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