Azizah, Siti (2016) Estimasi Parameter Model Smith Pada Max-Stable Process Spatial Extreme Value (Studi Kasus : Pemodelan Curah Hujan Ekstrem di Kabupaten Ngawi). Masters thesis, Institut Teknologi Sepuluh Nopember.
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Abstract
Curah hujan ekstrem yang tidak terduga dapat menyebabkan timbulnya bencana banjir. Prediksi curah hujan ekstrem perlu dilakukan agar upaya penanggulangan bencana banjir dapat tepat pada sasaran. Salah satu metode yang dapat memprediksi curah hujan ekstrem yaitu Spatial Extreme Value (SEV) dengan pendekatan Max-Stable Process (MSP). Salah satu hal yang penting dalam SEV adalah perhitungan return level (nilai ekstrem yang diprediksi). Perhitungan return level bergantung pada estimasi parameter dalam metode tersebut. Penelitian ini membahas tentang estimasi parameter dari Spatial Extreme Value Max-Stable Process khususnya model Smith. Estimasi parameter dilakukan menggunakan metode estimasi Maximum Composite Likelihood Estimation (MCLE) dan Maximum Pairwise Likelihood Estimation (MPLE). Hasil estimasi menggunakan metode ini tidak closed form, sehingga estimasi harus dilanjutkan menggunakan metode iterasi numerik. Metode iterasi yang digunakan pada penelitian ini adalah Broyden-Fletcher Goldfarb-Shanno (BFGS) Quasi Newton, yang lebih cepat mencapai konvergensi dibandingkan metode lain. Hasil dari estimasi parameter diterapkan pada data curah hujan Kabupaten Ngawi yang merupakan kabupaten dengan produksi pertanian padi terbesar di Provinsi Jawa Timur (provinsi dengan lahan pertanian padi terluas di Indonesia). Berdasarkan hasil analisis data diperoleh model trend surface µ ̂(s) = 2,794 0,242 v(s); σ ̂(s) = 1,8196 0,1106 v(s); ξ ̂(s) = 1,012 dengan ukuran kebaikan model Takeuchi Information Criterion (TIC) sebesar 26237,62. Nilai Root Mean Square Error (RMSE) berdasarkan 20 data testing sebesar 32,078 dan Mean Absolute Percentage Error (MAPE) sebesar 27,165%.
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The unpredictable extreme rainfall can affect flood. Prediction of extreme rainfall is needed to do, so that the efforts to preventing the flood can be effective. One of the methods that can predict the extreme rainfall is the Spatial Extreme Value (SEV) with the Max-Stable Process (MSP) approach. The important purpose of SEV is calculate of return level (the extreme value prediction). The calculation of return level depends on parameter estimation in that method. This research discusses about parameter estimation of the Spatial Extreme Value Max-Stable Process especially Smith model. Parameter estimation was performed using Maximum Composite Likelihood Estimation (MCLE) method dan Maximum Pairwise Likelihood Estimation (MPLE) method. The result of estimation using this method is not closed form, it must be continued by using numerical iteration method. The iteration method used in this research is Broyden-Fletcher Goldfarb-Shanno (BFGS) Quasi Newton, which is faster than other methods to achieve convergence. The result of parameter estimation applied to the rainfall data of Ngawi Regency which is the Regency with the largest rice production in East Java Province (the provice with the largest rice farm in Indonesia). Based on the results of data analysis obtained trend surface model µ ̂(s) = 2,794 + 0,242 v(s); σ ̂(s) = 1,8196 + 0,1106 v(s); ξ ̂(s) = 1,012 with goodness criterion model Takeuchi Information Criterion (TIC) 26237,62. Root Mean Square Error (RMSE) based on 20 testing data is 32,078 and Mean Absolute Percentage Error (MAPE) is 27,165%.
| Item Type: | Thesis (Masters) |
|---|---|
| Uncontrolled Keywords: | BFGS Quasi Newton; curah hujan ekstrem; likelihood estimation; Max-Stable Process; model Smith; return level; BFGS Quasi Newton; Smith model; extreme rainfall |
| Subjects: | H Social Sciences > HA Statistics Q Science > Q Science (General) |
| Divisions: | Faculty of Mathematics and Science > Statistics > 49101-(S2) Master Thesis |
| Depositing User: | Siti Azizah |
| Date Deposited: | 04 Apr 2017 04:40 |
| Last Modified: | 26 Dec 2018 06:45 |
| URI: | http://repository.its.ac.id/id/eprint/2548 |
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