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All Journal Jurnal Online Mahasiswa (JOM) Bidang Matematika dan Ilmu Pengetahuan Alam BAREKENG: Jurnal Ilmu Matematika dan Terapan Al-Muqayyad Operations Research: International Conference Series International Journal of Global Operations Research International Journal of Mathematics, Statistics, and Computing
Haposan Sirait
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Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation

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Estimation of the Three-Parameter Inverse Rayleigh Distribution Parameters for Guinea Pig Survival Data Faradila, Eky; Utari, Farah Asyifa; Zahra, Lathifah; Novitasari, Ratna; Astuti, Syaftiani Dwi; Sirait, Haposan
Operations Research: International Conference Series Vol. 6 No. 2 (2025): Operations Research International Conference Series (ORICS), June 2025
Publisher : Indonesian Operations Research Association (IORA)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.47194/orics.v6i2.384

Abstract

The Generalized Transmuted Inverse Rayleigh Function (GTIR) distribution is an extension of the inverse Rayleigh distribution, which is commonly used to model reliability and survival data. By incorporating an additional shape parameter (α) and a transmutation parameter (λ) alongside the scale parameter (σ), this distribution offers greater flexibility in handling skewed data or data with a non-monotonic hazard function. The parameters of the GTIR distribution are estimated using the Maximum Likelihood Estimation (MLE) method; however, they must be solved implicitly through numerical procedures. In this study, the GTIR distribution was employed to analyze the survival data of guinea pigs infected with tuberculosis. The primary objective of this analysis was to estimate the distribution parameters and to provide an overview of the survival pattern. The application of the GTIR distribution to the survival and hazard functions demonstrated that guinea pigs experience a sharp decline in survival probability at the onset of tuberculosis infection, followed by a gradual decrease in the risk of mortality over time. The hazard rate pattern, which initially increases and then decreases, indicates that the most critical period occurs immediately after infection. Parameter estimation of the GTIR distribution using the MLE approach yielded estimates of λ = 0.781, α = 10.135, and σ = 12.319, confirming that this model effectively captures the complex survival pattern with high accuracy.
ZILLMER RESERVE ON ENDOWMENT LAST SURVIVOR LIFE INSURANCE USING LOMAX DISTRIBUTION Hasriati, Hasriati; Rimisti, Pragista; Sirait, Haposan; Lily, Endang
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 17 No 4 (2023): BAREKENG: Journal of Mathematics and Its Applications
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol17iss4pp2367-2380

Abstract

This article discusses Zillmer's reserves for endowment last survivor of life insurance. Zillmer reserves are a type of modification of premium reserves which are calculated using prospective reserves and the Zillmer rate. In Zillmer reserves, loading which is the difference between gross premium and net premium in the first policy year is greater than standard loading. In this article, the life insurance used is endowment last survivor of life insurance, where the reserve calculation for last survivor status is calculated for 3 cases, namely, both participants survive until the end of the policy, participant x survive but participant y died, and participant y survive but participant x died. So the purpose of this research is to find a way to make the loading value in 3 cases on the dwiguna last survivor of life insurance Zillmer reserves smaller. To achieve this goal, this article uses the Lomax distribution with the parameters estimated using maximum likelihood estimation and then determined by a Newton-Raphson iteration method. Based on the illustration, even though in the first policy year in cases where both participants survive until the end of the policy there was still a negative loading, overall Zillmer's reserves in each case continues to increase over time
PROSPECTIVE RESERVE AND FULL PRELIMINARY TERM RESERVE ON ENDOWMENT LAST SURVIVOR LIFE INSURANCE USING CLAYTON COPULA Hasriati, Hasriati; Nayunda, Voundri Nindia; Sirait, Haposan; Hasbiyati, Ihda
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 4 (2024): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol18iss4pp2479-2490

Abstract

Combined life insurance is a type of insurance that protects two or more people who are related by family and is divided into two, namely joint-life life insurance and last-survivor life insurance. The last survivor life insurance is a condition of life insurance that will continue if there is at least one of all insurance participants who is still alive and will stop if all insurance participants die. The insurance company has to pay the benefit to the heirs of the insurance participant. When a claim occurs, the insurance company must prepare the reserve fee. The purpose of this research is to determine the amount of premium reserve of endowment last-survivor life insurance using prospective reserve and full preliminary term reserve. Full preliminary term reserve is one of the modified premium reserve calculations from Zillmer Reserve. To determine prospective reserve and full preliminary term reserve using the initial life annuity, single premium, and annual premium. Whereas the initial life annuity is influenced by the combined life and death opportunity of the insurance participants. Furthermore, the combined life and death opportunity of insurance participants will be obtained from Clayton copula and to obtain the parameter of Clayton copula, Rstudio software is used. Based on the result, the value of prospective reserves and full preliminary term reserves has increased every year and prospective reserves produce a greater value than full preliminary term reserves. If the insurance company uses this reserve calculation, the reserve that the company must prepare will increase every year. This is useful for insurance companies in predicting the amount of reserves they must have.
Co-Authors Anne Mudya Yolanda Ardini, Ananda Rizki Dwi Arisman Adnan Asti Ralita Sari Astuti, Syaftiani Dwi Aulia, Sartika Mega Endang Lily Faradila, Eky fitriani, selvi Gunawan, Chairani Hasriati Hasriati, Hasriati Irfansyah Irfansyah Nayunda, Voundri Nindia nurnisaa Okta Bella Syuhada Putri, Viona Sephia Rahmad Ramadhan Laska Rangkuti, Aisyah Azhari Ratna Novitasari Ratni Dakhyu Riko Febrian Rimisti, Pragista Rustam Efendi Rustam Efendi Salih, Yasir Sri Agustina, Sri Utari, Farah Asyifa Zahra, Lathifah