Comparative Analysis of Normality Tests: Integrating Classical and Contemporary Approaches

This study conducts a systematic evaluation of several normality tests, essential in statistical analyses and validating assumptions in diverse fields, including finance and energy. The primary contribution lies in extending the Jelito-Pitera test to detect deviations in light-tailed distributions, filling a gap in the range of existing normality tests. Additionally, this research conducts a detailed comparison of recent normality tests, specifically focusing on the Jelito-Pitera test and the Kullback-Leibler information-based test. We assess their effectiveness in identifying deviations not only in heavy-tailed but also in light-tailed distributions. Employing Monte Carlo simulations across various sample sizes and significance levels, our work examines the efficacy of well-established tests like Anderson-Darling, Zhang, Shapiro-Wilk, Shapiro-Francia, and Jarque-Bera, alongside these newer methods. The focus is on their per-formance in different non-normal distributions, aiming to understand their relative strengths and limitations in practical applications. The findings of this research provide a nuanced view of statistical testing methods, emphasizing the adaptation of the Jelito-Pitera test for light tails and offering insights into the comparative effectiveness of both classical and contemporary normality tests under diverse conditions. This study aims to assist researchers and practitioners in selecting the most suitable normality test for their data, thereby improving the precision of data analysis across various research areas.