A Novel Test of Fit Based on Phi-divergence with Real Data Application

Abstract

The paper presents a novel approach to estimating the Phi-divergence measure, accompanied bya detailed and thorough goodness-of-fit test. The proposed test exhibits valuable qualities suchas consistency and invariance, which have been rigorously established. To assess the effectivenessof the proposed test, an extensive simulation study is conducted. The study compares the per-formance of the proposed test with several well-known competing tests under various alternativescenarios involving exponential, Weibull, and log-normal distributions. This comparison allows fora comprehensive evaluation of the proposed test’s efficacy. Additionally, to provide a practicalunderstanding of the proposed methodology, two illustrative examples are included. These exam-ples serve as concrete demonstrations of how the proposed procedure can be applied in real-worldsituations