Pemodelan Risiko Ekstrem pada Kejadian Gempa Bumi di Indonesia Menggunakan Pendekatan Sub-Sampling Block Maxima

Azzahra, Annisa Fathimah (2026) Pemodelan Risiko Ekstrem pada Kejadian Gempa Bumi di Indonesia Menggunakan Pendekatan Sub-Sampling Block Maxima. Masters thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Extreme Value Theory (EVT) seringkali digunakan untuk menganalisis peristiwa ekstrem melalui ekor distribusi yang direpresentasikan oleh Extreme Value Index (EVI). Dalam estimasi EVI, pendekatan Block Maxima (BM) memiliki keterbatasan karena hanya memanfaatkan satu nilai maksimum setiap blok, sehingga sensitif terhadap pemilihan ukuran blok dan berpotensi mengabaikan informasi ekstrem lainnya. Oleh karena itu, penelitian ini mengkaji estimasi parameter EVI dalam pemodelan risiko ekstrem menggunakan metode Sub-sampling Block Maxima (SBM). Selain itu, penelitian ini juga membandingkan model BM dan SBM melalui Mean Absolute Percentage Error (MAPE) dan Root Mean Square Error (RMSE) pada analisis gempa bumi. Estimasi parameter EVI dilakukan menggunakan pendekatan Most Probable Maximum Risk (MPMR) dan Expected Maximum Risk (EMR). Hasil analisis menunjukkan bahwa data energi gempa bumi harian memiliki distribusi tidak simetris dengan ekor kanan yang panjang. Estimasi EVI menggunakan metode SBM menghasilkan nilai EVI lebih besar dari satu, yang menunjukkan karakteristik heavy-tailed dan berada dalam domain distribusi Fréchet. Hasil evaluasi menunjukkan bahwa pendekatan SBM menghasilkan estimasi return level dengan tingkat kesalahan yang lebih stabil, ditunjukkan oleh nilai MAPE sebesar 6,07% dan RMSE sebesar 0,45, sedangkan pada pendekatan BM nilai kesalahan bervariasi antar ukuran blok, dengan MAPE dan RMSE yang lebih besar dibanding SBM. Hasil ini menunjukkan bahwa SBM lebih konsisten dalam merepresentasikan risiko kejadian gempa bumi ekstrem pada data gempa bumi harian di Indonesia.
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Extreme Value Theory (EVT) is commonly used to analyze extreme events by examining the behavior of distribution tails, which are characterized by the Extreme Value Index (EVI). In estimating the EVI, the Block Maxima (BM) approach has limitations because it relies on only a single maximum value from each block, making it sensitive to the choice of block size and potentially overlooking other extreme information. Therefore, this study examines the estimation of the EVI parameter in extreme risk modeling using the Sub-sampling Block Maxima (SBM) method. In addition, the performance of the BM and SBM models is compared using the Mean Absolute Percentage Error (MAPE) and Root Mean Square Error (RMSE) in the analysis of earthquake data. The EVI parameter is estimated using the Most Probable Maximum Risk (MPMR) and Expected Maximum Risk (EMR) approaches. The results indicate that daily earthquake energy data exhibit an asymmetric distribution with a long right tail. EVI estimates obtained using the SBM method are greater than one, indicating heavy-tailed behavior and belonging to the Fréchet domain of attraction. The evaluation results show that the SBM approach provides more stable return level estimates, as reflected by a MAPE value of 6.07% and an RMSE of 0.45. In contrast, the BM approach produces error values that vary across block sizes, with MAPE and RMSE values generally higher than those obtained using SBM. These findings suggest that SBM offers a more consistent representation of the risk associated with extreme earthquake events in daily earthquake data in Indonesia.

Item Type:	Thesis (Masters)
Uncontrolled Keywords:	Expected Maximum Risk, Extreme Value Index, Extreme Value Theory, Gempa Bumi, Most Probable Maximum Risk ============================================================= Earthquake, Expected Maximum Risk, Extreme Value Index, Extreme Value Theory, Most Probable Maximum Risk
Subjects:	Q Science > QA Mathematics > QA273.6 Weibull distribution. Logistic distribution. Q Science > QA Mathematics > QA274.2 Stochastic analysis Q Science > QA Mathematics > QA276 Mathematical statistics. Time-series analysis. Failure time data analysis. Survival analysis (Biometry) Q Science > QA Mathematics > QA401 Mathematical models. Q Science > QE Geology > QE538.8 Earthquakes. Seismology
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49101-(S2) Master Thesis
Depositing User:	Annisa Fathimah Azzahra
Date Deposited:	31 Jan 2026 06:18
Last Modified:	31 Jan 2026 06:18
URI:	http://repository.its.ac.id/id/eprint/131396

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