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All Journal Teknosains: Media Informasi Sains dan Teknologi Jurnal Matematika dan Statistika serta Aplikasinya (Jurnal MSA) BAREKENG: Jurnal Ilmu Matematika dan Terapan JURNAL Al-AZHAR INDONESIA SERI HUMANIORA EIGEN MATHEMATICS JOURNAL Majalah Ilmiah Matematika dan Statistika (MIMS) Journal of Mathematics: Theory and Applications UNP Journal of Statistics and Data Science Al-Aqlu : Jurnal Matematika, Teknik dan Sains
Risnawati Ibnas
Universitas Islam Negeri Alauddin Makassar
Agriculture, Biological Sciences & Forestry Humanities Biochemistry, Genetics & Molecular Biology Civil Engineering, Building, Construction & Architecture Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Energy Engineering Environmental Science Mathematics Mechanical Engineering Medicine & Pharmacology Physics Social Sciences Transportation

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Penerapan Model Pertumbuhan Populasi Malthus dan Verhulst untuk Estimasi Jumlah Penduduk di Provinsi Sulawesi Selatan Fitria Syawal; Ilham Syata; Hikmawati Pathuddin; Risnawati Ibnas
Journal of Mathematics: Theory and Applications Vol 7 No 1 (2025): Volume 7, Nomor 1, 2025
Publisher : Program Studi Matematika Universitas Sulawesi Barat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31605/jomta.v7i1.4280

Abstract

Pertumbuhan jumlah penduduk merupakan pertambahan atau bertambahnya jumlah penduduk di suatu daerah dalam waktu tertentu. Peningkatan tersebut dapat menimbulkan dampak yang negatif bagi masyarakat , akan terjadi keseimbangan antara jumlah penduduk dan sumber daya yang tersedia. Oleh karena itu, perlu dilakukan estimasi untuk perencanaan pembangunan di masa yang akan datang. Penelitian ini membahas perbandingan model Malthus dan Verhulst sebagai model yang digunakan untuk memperkirakan jumlah penduduk di Provinsi Sulawesi Selatan berdasarkan kelompok umur dan jenis kelamin. Hasil dari perbandingan yang diperoleh bahwa model yang akurat untuk melakukan estimasi jumlah penduduk adalah model Verhulst. Hal ini diperoleh dari perhitungan masing-masing galat kedua model yaitu galat model Verhulst lebih kecil dari model Malthus yakni sebesar 4,34% penduduk laki-laki serta kelompok umurnya sebesar 1,77% sedangkan penduduk perempuan sebesar 3,20% dengan kelompok umur 1 ,12%. Hasil estimasi jumlah penduduk Provinsi Sulawesi Selatan menggunakan model Verhulst tahun 2033 diperkirakan akan mencapai 10.601.940 jiwa.
Modeling Tail Risk of Employment Injury Claims using the Extreme Value Theory Framework Sri Dewi Anugrawati; Nurwahidah; Nur Aeni; Risnawati Ibnas
UNP Journal of Statistics and Data Science Vol. 4 No. 3 (2026): UNP Journal of Statistics and Data Science
Publisher : Departemen Statistika Universitas Negeri Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24036/ujsds/vol4-iss3/480

Abstract

This study investigates the implementation of Extreme Value Theory (EVT) in modeling tail risk associated with employment injury insurance claims, addressing the critical need for robust risk estimation in the presence of rare, high-severity losses. The dataset consists of 1,177 historical claims from BPJS Ketenagakerjaan Makassar recorded between 2016 and 2023. Preliminary diagnostic procedures, including hill plots and mean excess function analysis, reveal heavy-tailed behaviour with a tail index greater than one, implying the possibility of infinite variance—a characteristic often underestimated by traditional actuarial models. Due to the limited number of extreme exceedances, the block maxima framework was adopted, and a Generalized Extreme Value (GEV) distribution was fitted to weekly maxima using L-moment estimation to ensure parameter convergence. The resulting GEV parameters (location = 50.27, scale = 67.19, shape = 0.443) confirm a Fréchet-type distribution, consistent with a heavy-tailed risk profile. Comparative analysis shows that the GEV-based 99.5% VaR (1,484.09 million IDR) is more than three times higher than the empirical estimate (450.56 million IDR). Return level analysis further contextualized the estimates, indicating a one-year return level of 768.51 million IDR. These findings demonstrate that empirical methods substantially underestimate extreme loss potential, potentially threatening insurer solvency. Overall, this study provides a statistically rigorous framework for capital reserve and reinsurance optimization, offering a more conservative and theoretically justified approach to managing catastrophic occupational risks.
Co-Authors Achmad Taufiq Adnan Sauddin Agustina, Nurwahyu Alda Alda Wahyuni Alfian Nurul Hidayat Andi Mariani Anugrawati, Sri Dewi Asfar, Asfar Chatarina Umbul Wahyuni Deni Candra Dewi, Riani Sinta Ermawati Ermawati Ermawati Fitria Syawal Ilham Syata Irwan Irwan Kasse juslifa, rezki eka wulandani Kirani, Azizah Fitrah Kurniawan, Baso Agung M. Ikhsan Amarta Mahda Al Maidah Mitra Aulia Ramli Muh Irwan Muh Irwan, Muh Muh. Irwan Muhammad Muhadir Aludin Muhammad Ridwan Muhammad Ridwan Musgani, Hijaz K Nawawi, M. Ichsan Nur Aeni Nur Azisa Nur Salam Nur Wirun, Nur Huda Nurfadilah, Khalilah Nurwahidah Nurwahidah Nurwahidah Orna Waty Faradilla Pathuddin, Hikmawati Putri Resky Hasyim Rasyid, Adiatma Riska Amalia Rismayanti Rosmaniar, Rosmaniar Satriani Satriani Satriani Satriani St. Hasna Nurfitriani Ula, Rahmatul Wa Ode Firda Sasmita Darwin Wahidah Alwi WS Athiyyah Hazimah Yunistira