基于尺度混合偏正态分布的考试成绩分析

Statistical Analysis for Exam Scores via Scale Mixture of Skew-Normal Distributions

摘要: 本文针对考试成绩分布多峰、有偏的特点，提出采用有限混合–尺度混合偏正态分布进行统计分析。通过模拟和实证分析，对比了多个潜在混合分布，证实所提方法的有效性。文章进一步采用有限混合–尺度混合偏正态误差回归模型对影响考试成绩的因素进行探讨，并与正态误差回归模型进行对比，证实混合偏正态误差回归模型在对考试成绩评价中的优势。

Abstract: This article proposes the use of finite mixture-scale mixture of skew-normal distributions for statistical analysis of exam scores that exhibit multiple peaks and skewness. Through simulation and empirical studies, multiple potential mixture distributions are compared to demonstrate the effectiveness of the proposed method. Furthermore, a linear regression model with a finite mixture-scale mixture of skew-normal error is used to investigate the factors influencing exam scores, and is compared with a normal error regression model, confirming the advantages of the mixture of skew-normal error regression model in evaluating exam performance.