Compositional datasets used in the application section of the Dirichlet distribution and its extension

Adult Urinary Excretion Data (steroids): Contains measurements of three steroid metabolites (cortisol, corticosterone, and pregnanetriol) in adult urine samples. The data is projected onto the positive orthant of a unit hypersphere. Fossil Pollen Composition Data (fossils): Includes proportions of three pollen types (Pinus, Abies, and Quercus) from various fossil samples, also projected onto the positive orthant of a unit hypersphere for this research. The urinary dataset exhibits negative correlations, while the fossil dataset shows both positive and negative correlations, allowing for comprehensive model evaluation. These datasets are valuable for researchers studying compositional data analysis, directional statistics, or developing new statistical models for data on the positive orthant of hyperspheres.

成人尿液排泄数据（类固醇）：包含成人尿液样本中三种类固醇代谢物（皮质醇、皮质酮和孕三醇）的测量值。数据被投射至单位超球体的正半轴。古生物学花粉组成数据（化石）：包括来自各种化石样本的三种花粉类型（松、云杉和栎）的比例，同样被投射至单位超球体的正半轴。尿液数据集表现出负相关性，而化石数据集则显示出正负相关性，从而为全面模型评估提供了可能。这些数据集对于研究组成数据分析、方向统计或开发针对单位超球体正半轴数据的全新统计模型的研究人员而言，具有重要的价值。