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All Journal Jurnal Geocelebes BAREKENG: Jurnal Ilmu Matematika dan Terapan JTAM (Jurnal Teori dan Aplikasi Matematika) APTEK Jurnal Politik Pemerintahan Dharma Praja Jurnal Ilmiah Matematika International Journal of Research in Community Services Publicness: Journal of Public Administration Studies Indonesian Journal of Community Empowerment and Service Proceeding International Conference on Mathematics and Learning Research
Jose Rizal
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Humanities Computer Science & IT Control & Systems Engineering Earth & Planetary Sciences Economics, Econometrics & Finance Education Energy Engineering Mathematics Mechanical Engineering Physics Social Sciences Transportation Other

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The Probability Model of Earthquake Frequency in the Enggano Segment using Poisson Mixture Models Yosmar, Siska; Rachmawati, Ramya; Damayanti, Septri; Rizal, Jose
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 1 (2026): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i1.33446

Abstract

An earthquake is a natural disaster that occurs suddenly resulting in numerous casualties, such as loss of life and property. Bengkulu Province is among the provinces affected by severe earthquakes. Studies on probability models for the frequency of earthquake events in Bengkulu Province are still scarce, as outlined in the 2017 book “Map of Sources and Hazards of Indonesian Earthquakes.” This research uses Poisson mixture models to build a probability model for the frequency of earthquake events in the Enggano segment, located in the coastal area of Bengkulu Province.   ..   The phases of model building are the model diagnosis phase, testing the dispersion state relative to the Poisson distribution, testing the dependence of research data on time variables using the Ljung-Box test, and testing the criteria for selecting the best model using the Bayesian Tests Measures of Information Criterion (BIC) and Akaike Information Criterion (AIC). Annual earthquake frequency data from January 1, 1971, to December 31, 2022, were retrieved from the USGS catalog of data on the frequency of major earthquakes with a magnitude of Mw ≥ 4.40, which occurred a total of 633 times. After completing the model building phase, the AIC and BIC values for each model were determined by determining the number of unobserved groups. Both Poisson mixture models and Poisson hidden Markov models produced the same number of unobserved groups of 3 groups with AIC=302.91 and BIC=324.38.
Comparative Analysis of SARIMA and SARIMAX Models for Rainfall Forecasting: A Case Study of Bandung City with Humidity as an Exogenous Variable Bella, Claudia Cantika; Rizal, Jose; Agwil, Winalia
Proceeding International Conference on Mathematics and Learning Research 2025: Proceeding International Conference on Mathematics and Learning Research
Publisher : Universitas Muhammadiyah Surakarta

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Abstract

Accurate rainfall forecasting is crucial in Indonesia, where climate change exacerbates the risks of droughts and floods. This study conducts a comparative analysis of Seasonal Autoregressive Integrated Moving Average (SARIMA) and its extension with exogenous variables (SARIMAX) to evaluate the impact of incorporating air humidity in rainfall prediction for Bandung City. Unlike SARIMA, which relies solely on univariate data, SARIMAX integrates external climatic factors, potentially enhancing predictive accuracy. This study analyzed monthly rainfall and air humidity data from January 2014 to December 2023. The modeling procedure included stationarity testing, seasonal decomposition, model identification using ACF and PACF diagnostics, parameter estimation via Maximum Likelihood Estimation (MLE), and residual diagnostic checks. Forecasting performance was comparatively evaluated using Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and Mean Absolute Scaled Error (MASE). The findings indicate that SARIMAX consistently outperforms SARIMA, yielding lower AIC and BIC values and achieving a MASE of 0.690 compared to 0.840 for SARIMA. This demonstrates that exogenous climatic variables play a crucial role in reducing forecasting error, particularly for seasonal and climate-sensitive time series. Beyond methodological contributions, the findings offer practical implications: incorporating humidity into forecasting models provides policymakers and disaster management authorities with more precise information for climate adaptation and risk mitigation strategies.
Co-Authors Acnesya, Vivin Agwil, Winalia Aldri Frinaldi Bella, Claudia Cantika Dwi Kumala, Siska Dzakirah, Qanitahudz Fachri Faisal Faisal, Fahri Firdaus Firdaus Hermalia, Hermalia Lestari, Wina Ayu Natisharevi, Raditya Janaloka Nooravieta Setiawan, Aisyah Nur Afandi Pepi Novianti Rafflesia, Ulfa Ramya Rachmawati Saiful Anwar Septa, Oon Septri Damayanti Sigit Nugroho Siska Yosmar Sunandi, Etis Suripto, Heri Syahada, Sri Widayati, Ratna