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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 Quantitative Research and Modeling 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 Environmental Science 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.
Premium Sufficiency Reserve on Joint Life Insurance with Laplace Distribution Triyuni, Meisy; Sirait, Haposan
International Journal of Quantitative Research and Modeling Vol. 6 No. 3 (2025): International Journal of Quantitative Research and Modeling (IJQRM)
Publisher : Research Collaboration Community (RCC)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.46336/ijqrm.v6i3.1074

Abstract

Each insurance participant pays a premium to the insurance company during the coverage period. In paying the sum insured to insurance participants, insurance companies need to prepare reserve costs. This reserve fee is used to pay for the needs of insurance companies and insurance participants. This research explains the calculation of premium sufficiency reserve for joint life insurance for life insurance participants aged x years and y years with Laplace distribution. The parameters of the Laplace distribution are estimated using the method of momen and the method of maximum likelihood. The solution of the problem is obtained by determining the initial life annuity term, single premium, and annual premium so that the premium sufficiency reserve formula based on Laplace distribution is obtained. The results of the calculation of premium sufficiency reserves of joint life insurance using Laplace distribution are more less the same as the prospective reserves of joint life insurance using Laplace distribution.
Application of Structural Equations Modeling Partial Least Square at the Comparation of the Niveau of Responsibility From Cs and Digics Pradana, Visca Nadia; Sirait, Haposan
International Journal of Quantitative Research and Modeling Vol. 5 No. 1 (2024)
Publisher : Research Collaboration Community (RCC)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.46336/ijqrm.v5i1.604

Abstract

Banking is an institution that plays a role in increasing economic development and also increasing equitable development. People who are serving users will be more selective in choosing banks so that many banks strive to be superior and more satisfying than other banks. Customer satisfaction can be seen from the role of CS and DigiCS. Customer Service ( CS ) is all actions intended to meet needs and activities by providing services so that each customer's needs are met. Digital Customer Service (DigiCS) is BNI digital banking automation that provides customers with immediate experience when carrying out digital transactions at BNI . The aim of this research is to determine the factors that influence the level of CS and DigiCS customer satisfaction with several variables, namely product quality ( ), service quality ( ), time ( ), convenience/efficiency ( ), and customer satisfaction (Y). The method used in this research is structural equation modeling partial least squares with the help of Microsoft Excel and SmartPLS software with the application of SEM - PLS to analyze the relationship between endogenous latent variables and exogenous latent variables. The results of this research are that for CS customer satisfaction it is found that only the exogenous variable product quality ( ) with its influences indicators customer satisfaction (Y) while for DigiCS customer satisfaction the results are that only the exogenous variable product quality ( ) and the exogenous variable convenience/efficiency ( ) with indicators that influence customer satisfaction (Y).
Survival Analysis of Patients with Kidney Failure at Arifin Achmad Hospital, Riau Province using the Kaplan-Meier Method Sanurtillah, Farissa; Sirait, Haposan
International Journal of Quantitative Research and Modeling Vol. 5 No. 2 (2024)
Publisher : Research Collaboration Community (RCC)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.46336/ijqrm.v5i2.689

Abstract

The importance of applying advanced mathematical models in bond investing marks a revolutionary step in the modern financial industry, enabling more scalable and adaptive strategies to achieve financial success. The purpose of this talk is to explore and detail the role of advanced mathematical models in changing the bond investment paradigm. The discussion aims to highlight the crucial role of advanced mathematical models in changing the bond investment paradigm, providing a deeper understanding of the optimal potential and risks involved, explaining how this approach can optimize financial outcomes through more detailed analysis. The application of mathematical models involves the use of sophisticated algorithms and statistical analysis to identify optimal investment opportunities. These steps include the use of advanced financial math formulas, such as yield to maturity and duration, to design investment strategies that are adaptive and responsive to bond market dynamics. The application of mathematical models results in a deeper understanding of the bond market, allowing investors to respond quickly to changing market conditions. Thus, the investment strategy formed by this approach can not only improve investment returns, but also reduce the risks that investors may face. The application of advanced mathematical models in bond investing opens the door to smarter and more informed decision-making. By combining data and mathematical analysis, investors can maximize potential investment returns and manage risks more effectively.
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 Pradana, Visca Nadia Putri, Viona Sephia Rahmad Ramadhan Laska Rangkuti, Aisyah Azhari Ratna Novitasari Ratni Dakhyu Riko Febrian Rimisti, Pragista Rustam Efendi Rustam Efendi Salih, Yasir Sanurtillah, Farissa Sri Agustina, Sri Triyuni, Meisy Utari, Farah Asyifa Zahra, Lathifah