Clustering and Mixture Distribution Analysis of Average Years of Schooling in Papua (2010–2023) - Alvian Sroyer; Henderina Morin; Felix Reba; Jonathan Wororomi; Agustinus Languwuyo (CAUCHY: Jurnal Matematika Murni dan Aplikasi, 2025)
The purpose of this research is to analyze the distribution of the Human Development Index (HDI) in Papua based on the average years of schooling during the 2010–2023 period using the Gaussian Mixture-based Clustering approach. Data from 28 districts are grouped into five clusters according to their distributional characteristics. Each cluster is modeled using one of the four probability distributions: Inverse Gaussian, Rician, Weibull, or Nakagami. Parameter estimation was performed using the Maximum Likelihood Estimation (MLE) method, and the best distribution for each cluster was selected based on several information criteria (AIC, BIC, AICc, CAIC, and HQC) and validated through Kolmogorov-Smirnov (KS) and Anderson-Darling (AD) tests. The analysis results show that the Inverse Gaussian distribution fits Cluster 1 and Cluster 3, which represent districts with lower HDI schooling patterns. Cluster 2 is best described by the Rician distribution, indicating moderate HDI variability. The Weibull distribution fits Cluster 4, representing areas with moderately improving education. Cluster 5, with the highest and most stable HDI levels, is best modeled using the Nakagami distribution. The resulting mixture model, combining these four distributions, accurately reflects the HDI distribution patterns across Papua. Policy implications from this study include the development of cluster-based educational strategies tailored to regional characteristics to improve educational equity and human development across the province.