Goodness-of-Fit Test for Exponentiality Based on Kullback–Leibler Information

Abstract

Abstract In this paper, we discuss goodness-of-fit tests of the exponential distribution based on Kullback–Leibler information. To construct test statistics, Van Es' and Correa's entropy estimator are used as an estimator of Shannon's entropy. Critical values for various sample sizes determined by means of Monte Carlo simulations are presented for each of test statistics. Also, formulas for calculating approximate critical values for given sample sizes are provided for the respective test statistics. A Monte Carlo power analysis is performed for various alternatives and sample sizes in order to compare the proposed tests with several existing goodness-of-fit tests based on the empirical distribution function (EDF). Simulation results show that Kullback–Leibler information tests have higher powers than the EDF tests.