A New Goodness-of-Fit Test for Azzalini's Skew-<em>t</em> Distribution Based on the Energy Distance Framework with Applications

In response to the growing need for flexible parametric models for skewed and heavy-tailed data, this paper introduces a novel goodness-of-fit test for the Skew-$t$ distribution, a widely used flexible parametric probability distribution. Traditional methods often fail to capture the complex behavior of data in fields such as engineering, public health, and the social sciences. Our proposed test, based on energy statistics, provides a robust and powerful tool for practitioners to assess the suitability of the Skew-$t$ distribution for their data. We present a comprehensive methodological evaluation, including a comparative study that highlights the advantages of our approach over traditional tests. The results of our simulation studies demonstrate a significant improvement in power, leading to more reliable inference. To further showcase the practical utility of our method, we apply our test to two real-world datasets, offering a valuable contribution to both the theoretical and applied aspects of statistical modeling for non-normal data.