Life Table Prediction Using the Lee-Carter Model

Putu Zeni Candrika Kertayanda, Tiara Yulita, Dila Tirta Julianty, Annastasya Ginting, Mei Nalda Adelia Simanjuntak

Abstract


Mortality is the state where all signs of life permanently, which can occur at any time after a person is born. Mortality data can be presented in the form of table called a mortality table, which is a table that provides an overview of the life of a population group starting from births at the same time and life of a population group that starts from birth at the same time and slowly decreases due to death. In actuarial studies, this table has a role as one of the important factors to determine the amount of premium costs and premium reserves, especially life insurance. Therefore, it is necessary for continuity in conducting research related to mortality tables. This research aims to forecast the death rate and the probability of death of the population in the future using the Lee-Carter model, which is a mortality forecasting model that combines a demographic model with a time series model. This mortality model shows that the logarithm of mortality rate is the sum of the parameters of the average general mortality rate by age and the multiplication of the trend parameter of mortality rate changes by age with the mortality index parameter. Forecasting process begins with estimating the parameters of the average mortality rate and the trend of mortality rate changes influenced by the mortality index parameter using the singular value decomposition (SVD) method. After that, the mortality index mortality index is forecasted using the ARIMA model and the results of this forecast are then reinserted into the Lee-Carter model to obtain death rate prediction. Based on the results of the mortality rate prediction, it can then be the prediction of the probability of death for the mortality table. The result of this research is a mortality table that contains predictions of the probability of death of the Indonesian population for both male and female gender using the Lee-Carter model from the year 2022 2026. Based on these results, it is concluded that the value of the probability of death for each year increases with increasing age.

Full Text:

PDF

References


R. Unaeni, N. Setyahadewi and H. Perdana, "Peramalan Tingkat Kematian (Mortalita) Menggunakan Model Lee Carter," Buletin Ilmiah Math. Stat. dan Terapannya (Bimaster), vol. 6 (1), pp. 9-18, 2017.

H. Utomo, "Perbandingan Tabel Mortalita Indonesia dan Tabel Mortalita CSO Menggunakan Uji Mann-Whitney dan Uji Kruskal-Wallis," Syntax Literate: Jurnal Ilmiah Indonesia, vol. 6 (3), p. 1210, 2021.

R. K. Thomas, Concepts, Methods and Practical Applications in Applied Demography: An Introductory Textbook, Switzerland: Springer Cham, 2018.

P. Omas Bulan Samosir, S. Rihlah Romdoniah and S. Israul Hasanah, Konsep dan Ukuran Mortalitas, Jakarta: Badan Kependudukan dan Keluarga Berencana Nasional, 2020.

F. N. F. Sudding, "Pengaruh Asumsi Stokastik Mortalita Lee-Carter dan Asumsi Deterministik Gompertz Terhadap Nilai-Nilai Anuitas, Santunan, dan Premi," M.S. thesis, Institut Teknologi Bandung, 2014.

L. Yang, Strength and Weakness of Lee-Carter Models, Netherlands: Maastricht University, 2019.

Y. H. Umar and U. J. Chukwudi, "Modeling Mortality Rates Using Heligman-Pollard and Lee-Carter in Nigeria," American Journal of Theoritical and Applied Statistics, vol. 8 (6), pp. 221-239, 2019.

N. S. M. Ibrahim, N. M. Lazam and S. N. Shair, " Forecasting Malaysian Mortality Rates Using the Lee-Carter Model with Fitting Period Variants," Journal of Physics: Conference Series, p. 9, 2021.

I. Nursaadah, E. Puspita and R. Marwati, "Metode Peramalan Mortalita Menggunakan Metode Lee-Carter," EurekaMatika, vol. 3 (1), pp. 17-30, 2015.

A. Sitanggang, A. D. Harahap, A. Karimullah, Y. A. Dewantara and C. Rozikin, "Sistem Rekomendasi Anime Menggunakan Metode Singular Value Decomposition (SVD) dan Cosine Similarity," Jurnal Teknologi Informasi, vol. 2(2), pp. 90-94, 2023.

F. Girosi and G. King, "Understanding the Lee-Carter Mortality Forecasting Method," 2007.

F. Dick London, Survival Models and Their Estimation Third Edition, ACTEX Publications, 1997.

F. Fejriani, M. Hendrawansyah, L. Muharni, S. F. Handayani and Syaharuddin, "Forecasting Peningkatan Jumlah Penduduk Berdasarkan Jenis Kelamin Menggunakan Metode ARIMA," Jurnal Kajian Geography, vol. 8 (1), pp. 28-29, 2020.

S. P. Fauzani and D. Rahmi, "Penerapan Metode ARIMA dalam Peramalan Harga Produksi Karet di Provinsi Riau," Jurnal Teknologi dan Manajemen Industri Terapan, vol. 2 (4), pp. 269-277, 2023.

W. Rusyida and V. Pratama, "Prediksi Harga Saham Garuda Indonesia di Tengah Pandemi Covid-19 Menggunakan Metode ARIMA," SQUARE: Journal of Mathematics and Mathematics Education, vol. 2 (1), p. 75, 2020.

J. Purnama and A. Juliana, "Analisa Prediksi Indeks Harga Saham Gabungan Menggunakan Metode ARIMA," Cakrawala Management Business Journal, vol. 2 (2), p. 459, 2019.

W. W. S. Wei, Time Series Analysis Univariate and Multivariate Methods Second Edition, United States: Pearson Addison Wesley, 2005.

T. Yunita, "Peramalan Jumlah Penggunaan Kuota Internet Menggunakan Metode Autoregressive Integrated Moving Average (ARIMA)," JOMTA Journal of Mathematics: Theory and Applications, vol. 1 (2), pp. 17-18, 2019.

S. M. I Wayan Sumarjaya, Modul Analisis Deret Waktu, Bukit Jimbranan, 2016.

N. A. Wijoyo, "Peramalan Nilai Tukar Rupiah Terhadap USD dengan Menggunakan Model GARCH," Kajian Ekonomi Keuangan, vol. 20 (2), p. 182, 2016.

S. Makridakis, S. C. Wheelwright and R. J. Hyndman, Metode dan Aplikasi Peramalan Edisi Kedua, Jakarta: Erlangga, 1995.

R. Agustini, N. Hajarisman and S. Sunendiari, "Kriteria Pemilihan Model Peramalan Terbaik Berdasarkan Kriteria Informasi," Prosiding Statistika, vol. 4 (1), pp. 57-64, 2018.

J. D. Cryer and K.-S. Chan, Time Series Analysis With Applications in R, 2nd ed, New York: Springer, 2008.




DOI: http://dx.doi.org/10.33021/jafrm.v3i1.5429

DOI (PDF): http://dx.doi.org/10.33021/jafrm.v3i1.5429.g1969

Refbacks

  • There are currently no refbacks.