Dugasa Shibiru Jabessa, Arero Butte Gotu
Department of Mathematics, Kotebe University of Education, Addis Ababa, Ethiopia.
Department of Statistics, Addis Ababa University, Addis Ababa, Ethiopia.
PLoS One. 2025 Jul 24;20(7):e0328942. doi: 10.1371/journal.pone.0328942. eCollection 2025.
Cognitive achievements in mathematics skill scores are crucial for daily life in modern society. The objectives of this study were to apply the alpha power transformed Lindley probability distribution to students' cognitive achievement skill scores using regression models and to identify the best probability distributions for cognitive achievement, including APTLD, using Young Lives datasets. This study proposes regression modeling using the alpha power transformation Lindley probability distribution for the application of cognitive achievement in mathematics skill scores. The study found that students' average mathematics skill score was 37.01%, with a standard deviation of 14.9, reflecting performance variation. Parental education differed significantly, with 48.5% of mothers and 34% of fathers lacking formal schooling. Additionally, 59% of students lived in rural areas, while 41% resided in urban settings. The average household size was 5.77 members, showing variability in family structures. From the results, the findings show that the mean cognitive achievement in mathematics skill scores (37.01) is greater than the median (33.33), indicating that the data are positively skewed or right-skewed. The APTLD regression model demonstrates the best fit for the data, as indicated by its lowest AIC and BIC values compared to the APTEPLD, TPLD, and TwPLD models. This confirms its superiority in capturing the underlying structure of mathematics skill scores, making it the most suitable model for analyzing cognitive achievement. Therefore, this new model can be considered a significant contribution to the field of statistics and probability methods. Future work on the presented study could extend the APTLD distribution using Bayesian regression models.
数学技能分数方面的认知成就对现代社会的日常生活至关重要。本研究的目的是使用回归模型将α幂变换林德利概率分布应用于学生的认知成就技能分数，并使用“青少年生活”数据集确定包括α幂变换林德利概率分布（APTLD）在内的认知成就的最佳概率分布。本研究提出使用α幂变换林德利概率分布进行回归建模，以应用于数学技能分数方面的认知成就。研究发现，学生的平均数学技能分数为37.01%，标准差为14.9，反映了成绩的差异。父母的教育程度差异显著，48.5%的母亲和34%的父亲未接受过正规教育。此外，59%的学生生活在农村地区，41%居住在城市地区。平均家庭规模为5.77人，显示出家庭结构的差异。从结果来看，研究结果表明，数学技能分数方面的平均认知成就（37.01）大于中位数（33.33），这表明数据呈正偏态或右偏态。与α幂变换指数幂林德利分布（APTEPLD）、变换帕累托林德利分布（TPLD）和双参数韦布尔林德利分布（TwPLD）模型相比，APTLD回归模型的AIC和BIC值最低，表明其对数据的拟合最佳。这证实了其在捕捉数学技能分数潜在结构方面的优越性，使其成为分析认知成就最合适的模型。因此，这个新模型可被视为对统计和概率方法领域的重大贡献。关于本研究的未来工作可以使用贝叶斯回归模型扩展APTLD分布。
