Comparing the Power of Test of Exponential with Prominent Tests against Alternative with Various Kurtosis

Abstract

Aims. In this article, we propose a goodness of fit test for the exponential distribution based on some characterization of the exponential distribution. Methods. The test is a weighted integral of the squared distance between the integrated distribution function (IDF) and its estimate. A closed form for the test statistic is derived. The mean and variance of the test statistic are derived under the exponentiality assumption. Also, based on Monte Carlo simulations, the power of the test is evaluated at significance level α=0.05 for several sample sizes n=5,10,20, and 50. Results. The proposed test  T_1.5 is a good competitor of other known exponentiality test statistics. Conclusion. it is recommended to use a proposed test when testing a goodness-of-fit for exponential distribution. Specially, against distributions with kurtosis lower than exponential distribution.