A novel estimator of Kullback-Leibler information with its application to goodness of fit tests

Abstract

In this study, our primary focus is on introducing a new estimator of Kullback-Leibler information, which we subsequently utilize for conducting goodness-of-fit tests. We employ this new estimator to propose tests specifically tailored for assessing the fit of data to the normal, exponential, and Weibull distributions. To ensure the reliability and accuracy of our proposed tests, we utilize a Monte Carlo simulation approach. Through this simulation, we obtain percentile points and determine the type I error rates of the tests. This enables us to assess the performance and suitability of the proposed tests under different scenarios. Furthermore, we conduct a comprehensive simulation study to evaluate the power and effectiveness of our proposed tests. We compare their performance with that of other competing tests, allowing us to gauge their relative strengths and weaknesses. To demonstrate the practical applicability of the proposed tests, we provide three real data examples. These examples serve as illustrations of how the tests can be implemented and offer insights into their performance when applied to real-world data. By combining theoretical developments, simulation studies, and real data analysis, we aim to provide a comprehensive evaluation of the proposed goodness-of-fit tests based on the new estimator of Kullback-Leibler information.