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

Accepted - September 2024

Abstract

The paper presents a novel approach to estimating the Phi-divergence measure, accompanied by a detailed and thorough goodness-of-fit test. The proposed test exhibits valuable qualities such as consistency and invariance, which have been rigorously established. To assess the effectiveness of the proposed test, an extensive simulation study is conducted. The study compares the performance of the proposed test with several well-known competing tests under various alternative scenarios involving exponential, Weibull, and log-normal distributions. This comparison allows for a comprehensive evaluation of the proposed test’s efficacy. Additionally, to provide a practical understanding of the proposed methodology, two illustrative examples are included. These examples serve as concrete demonstrations of how the proposed procedure can be applied in real-world situations.