A Comparison of Generalized Pareto and Weibull Distributions for Modeling Megathrust Seismic Hazard in Indonesia

Aimmatul Ummah Alfajriyah (Department of Actuarial Science, Institut Teknologi Sepuluh Nopember, Surabaya, Indonesia)
Moch Taufik Hakiki (Department of Actuarial Science, Institut Teknologi Sepuluh Nopember, Surabaya, Indonesia)
Muhammad Haekhal Aqila (Department of Actuarial Science, Institut Teknologi Sepuluh Nopember, Surabaya, Indonesia)

Zero : Jurnal Sains, Matematika, dan Terapan
Vol 10, No 2 (2026): Zero: Jurnal Sains Matematika dan Terapan

Mapping extreme earthquake risks in Indonesia's megathrust zones is critical for disaster mitigation. This study compares the Generalized Pareto (GPD) and Weibull distributions in modeling extreme earthquake magnitude probabilities. We analyzed 74,514 events (Mw>5.5) across 16 megathrust segments from 1973 to 2024. This data representing a comprehensive large-scale analysis at the national level. To ensure statistical independence of observations, a declustering algorithm was applied to isolate mainshocks. Parameters were estimated using Maximum Likelihood Estimation (MLE) via Nelder-Mead optimization, and evaluated using PDF/CDF plots, AIC, and Cramer-von Mises statistics. Results indicate a significant disparity: the Weibull distribution failed to fit any of the segments, whereas the GPD proved suitable for all 16. Consistently lower AIC and test statistics confirm the GPD's superior accuracy in representing extreme magnitude patterns. Furthermore, return periods and corresponding return levels were calculated to explicitly quantify future extreme seismic hazards.