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.