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Pemodelan Besar Klaim menggunakan Distribusi Berekor dan Tail-Value-at-Risk (TVaR) pada Data Sampel Badan Penyelenggara Jaminan Sosial (BPJS) Kesehatan Widodo, Vicko Regenio; Adiyansyah, Firman; Anwar, Yusril Rais; Sari, Kurnia Novita
Jurnal Statistika dan Aplikasinya Vol. 7 No. 2 (2023): Jurnal Statistika dan Aplikasinya
Publisher : LPPM Universitas Negeri Jakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21009/JSA.07203

Abstract

Information about amount of insurance claims is needed by insurer to set premium or other decisions in the future. Amount of claims modeling is a way to determine the characteristics of a distribution of claims data and can be used to predict the amount of claims that may occur. A commonly used model for amount of insurance claims data is the distribution model for heavy tails. The discussion in this article focuses on modeling amount of insurance claims using Lognormal, Pareto and Weibull distributions, and also using Gamma distribution for comparison. The data used is sample data from Badan Penyelenggara Jaminan Sosial (BPJS) Kesehatan in 2015-2016. The data contains membership data and details of the amount of each participant's claim. The analysis is carried out to find out the best candidate model that matches the amount of insurance claims data for both inpatient and outpatient categories. In addition, the Tail-Value-at-Risk (TVaR) of the model will be calculated to determine the amount of capital that will be required with a 75% confidence level. Based on the results of the study, the best model for large data samples of claims for outpatient and inpatient categories is the Lognormal model. TVaR for the outpatient category is Rp492,596 and for the inpatient category is Rp7,672,726.
CONSTRUCTION OF INDONESIA MORBIDITY TABLE FOR GENITOURINARY SYSTEM-RELATED DISEASES TO FACILITATE INDONESIA’S ECONOMIC EXPANSION Sari, Kurnia Novita; Adiyansyah, Firman; Sergio, Steven; Antonius, Enrico
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 3 (2024): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol18iss3pp1549-1562

Abstract

The disease of the genitourinary system is one of the most common diseases in Indonesia. The disease shows some risk, especially in health and economic aspect. To overcome the risk posed by disease of the genitourinary system, a morbidity table can be used to reduce the number of people infected by the disease, and in this research, morbidity table based on sample data of BPJS Kesehatan from 2015 to 2016 will be constructed. Data processing starts with obtaining the empirical probability value of the disease of the genitourinary system. Then, the result obtained was interpolated in numerous preferences of methods. After the best interpolation model was known, the extrapolation process was run at an age range from age 80 to age 85 using Whittaker-Henderson smoothing method. The age range chosen is due to the fact that for ages over 80 years, the number of exposures is minimal, which can affect the number of claims in that age group. Extrapolation is extended up to the age of 85 years because the Morbidity Table for Critical Illness sets the age of 85 years as the upper limit for extrapolation. The model derived from interpolating age groups with a knot shows the highest R-square value, making it the most optimal model. It shows that Indonesians' probability to contract the disease is increasing significantly from about age 25 until around age 65, and the probability slowly declines after age 65. This result can be used as a reference by the Government of Indonesia to produce regulations leading to health protection for all citizens of Indonesia, especially for those who are classified as the labor force. Health protection provided by the government should improve welfare in Indonesian society. Moreover, the regulation should protect the productivity of the manpower and raise Indonesia’s Gross Domestic Product (GDP). BPJS Kesehatan can also use this predicted morbidity table to determine the right contribution fee. Hence, the contribution can be beneficial to pay any expense of the patient who contracted the disease, but on the other hand, not sending BPJS Kesehatan into bankruptcy. All of abovementioned efforts have one bold intention—to support Indonesia’s economic expansion as Indonesia aims to reach Golden Indonesia Vision by 2045.