Fauziyah, Meirinda (2020) Pemodelan Spatial Extreme Value Menggunakan Pendekatan Students's t Copula (Study Kasus: Pemodelan Curah Hujan di Kabupaten Ngawi). Masters thesis, Institut Teknologi Sepuluh Nopember.
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Abstract
Cuaca ekstrem merupakan kejadian cuaca yang tidak normal, jarang terjadi, dan jarang dapat dihindari. Akibatnya, dampak kerugian yang ditimbulkan pun cukup signfikan bagi lingkungan dan masyarakat. Dampak tersebut dapat diminimalisir dengan mempelajari pola dan karakteristik dari kejadian ekstrem tersebut. Metode statistika yang dikembangkan untuk mengidentifikasi kejadian ekstrem yaitu Extreme Value Theory (EVT). Kejadian ekstrem terjadi tidak hanya pada satu lokasi (univariat), namun dapat terjadi di beberapa lokasi (multivariat), sehingga data curah hujan termasuk data multivariat yang diukur berdasarkan lokasi atau mengikuti kaidah data spasial. Berdasarkan hal tersebut, diperoleh pengembangan ilmu mengenai Spatial Extreme Value (SEV). Beberapa pendekatan spasial yang digunakan adalah Max-Stable Process (MSP) dan Copula. Copula merupakan suatu fungsi dari dua hubungan distribusi yang masing-masing memiliki fungsi marjinal distribusi. Penelitian ini menggunakan pendekatan copula dengan jenis student’s t copula, karena distribusi multivariat t bersifat ekor gemuk (fat joint tail) yang mengindikasikan bahwa metode ini tepat digunakan pada data yang bersifat heavy tail. Metode ini memodelkan dependensi ekstremal antar lokasi dengan mentransformasi distibusi marjinal nilai ekstrem ke distribusi Frechet, kemudian ke unit copula. Penelitian ini dilakukan untuk memodelkan curah hujan ekstrem di Kabupaten Ngawi dengan pendekatan student’s t copula. Data yang digunakan untuk menyusun model dan estimasi parameter adalah data curah hujan tahun 1989-2010, sedangkan untuk validasi model menggunakan data tahun 2011-2015. Hasil penelitian menunjukkan bahwa estimasi SEV dengan PMLE diketahui penyelesaiannya tidak close form, sehingga dilanjutkan dengan metode iterasi numerik BFGS Quasi-Newton. Nilai extremal coefficient berada pada kisaran 1,4 hingga 1,7 hal ini berarti masih terdapat dependensi spasial antar pos hujan. Validasi model dilakukan dengan mengestimasi return level tahun 2011-2015 melalui pendekatan model student’s t copula. Nilai Root Mean Square Error (RMSE) yang diperoleh berdasarkan 20 blok data testing sebesar 34,917.
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Extreme weather is an abnormal weather event, rare, and rarely can be avoided. As a result, the impact of the losses caused is quite significant for the environment and society. However, the impacts can minimized by studying the patterns and characteristics of extreme events. The statistical method developed to identify extreme events is Extreme Value Theory (EVT). Extreme events can occur not only in one location (univariate), but can occur in several locations (multivariate) so that rainfall data including multivariate data measured by location or following the rules of spatial data. Therefore, the development of knowledge about Spatial Extreme Value (SEV) is obtained. Some spatial approaches that can be used are Max-Stable Process (MSP) and Copula. Copula is a function of two distribution relationships, each of which has a marginal distribution function. This study uses a copula approach with type student's t copula, because the multivariate distribution is fat joint (fat joint tail) which indicates that method is appropriate for heavy tail data such as extreme rainfall. This method models the extremal dependencies between locations by transforming the marginal distribution of extreme values to the Frechet distribution, then to the copula unit. This study examines the spatial extreme value modeling in Ngawi Regency with the student's t copula approach. The data used to construct the model and parameter estimation is the rainfall data for 1989-2010, while for the validation of the model using the data for 2011-2015. The results showed that estimated SEV with PMLE revealed the solution was not closed form, so it was continued with the numeric iteration method is Quasi-Newton BFGS. The value of extremal coefficient is in the range of 1,4 to 1,7, that means there are still spatial dependencies between rain stations. Model validation is done by estimating the 2011-2015 return level through the student's t copula model approach. The value of Root Mean Square Error (RMSE) obtained based on 20 blocks of testing data is 34,917.
| Item Type: | Thesis (Masters) |
|---|---|
| Additional Information: | RTSt 519.24 Fau p-1 2020 |
| Uncontrolled Keywords: | Curah hujan ekstrem, Extreme Value Theory, Spatial Extreme Value, Student’s t copula |
| Subjects: | H Social Sciences > HA Statistics > HA30.6 Spatial analysis H Social Sciences > HA Statistics > HA31.7 Estimation |
| Divisions: | Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49101-(S2) Master Thesis |
| Depositing User: | Meirinda Fauziyah |
| Date Deposited: | 12 Nov 2024 01:53 |
| Last Modified: | 12 Nov 2024 01:53 |
| URI: | http://repository.its.ac.id/id/eprint/74206 |
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