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BAREKENG: Jurnal Ilmu Matematika dan Terapan
Published by Universitas Pattimura
ISSN : 19787227     EISSN : 26153017     DOI : https://search.crossref.org/?q=barekeng
Core Subject : Economy, Science, Education, Engineering,
Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation
BAREKENG: Jurnal ilmu Matematika dan Terapan is one of the scientific publication media, which publish the article related to the result of research or study in the field of Pure Mathematics and Applied Mathematics. Focus and scope of BAREKENG: Jurnal ilmu Matematika dan Terapan, as follows: - Pure Mathematics (analysis, algebra & number theory), - Applied Mathematics (Fuzzy, Artificial Neural Network, Mathematics Modeling & Simulation, Control & Optimization, Ethno-mathematics, etc.), - Statistics, - Actuarial Science, - Logic, - Geometry & Topology, - Numerical Analysis, - Mathematic Computation and - Mathematics Education. The meaning word of "BAREKENG" is one of the words from Moluccas language which means "Counting" or "Calculating". Counting is one of the main and fundamental activities in the field of Mathematics. Therefore we tried to promote the word "Barekeng" as the name of our scientific journal also to promote the culture of the Maluku Area. BAREKENG: Jurnal ilmu Matematika dan Terapan is published four (4) times a year in March, June, September and December, since 2020 and each issue consists of 15 articles. The first published since 2007 in printed version (p-ISSN: 1978-7227) and then in 2018 BAREKENG journal has published in online version (e-ISSN: 2615-3017) on website: (https://ojs3.unpatti.ac.id/index.php/barekeng/). This journal system is currently using OJS3.1.1.4 from PKP. BAREKENG: Jurnal ilmu Matematika dan Terapan has been nationally accredited at Level 3 (SINTA 3) since December 2018, based on the Direktur Jenderal Penguatan Riset dan Pengembangan, Kementerian Riset, Teknologi, dan Pendidikan Tinggi, Republik Indonesia, with Decree No. : 34 / E / KPT / 2018. In 2019, BAREKENG: Jurnal ilmu Matematika dan Terapan has been re-accredited by Direktur Jenderal Penguatan Riset dan Pengembangan, Kementerian Riset, Teknologi, dan Pendidikan Tinggi, Republik Indonesia and accredited in level 3 (SINTA 3), with Decree No.: 29 / E / KPT / 2019. BAREKENG: Jurnal ilmu Matematika dan Terapan was published by: Mathematics Department Faculty of Mathematics and Natural Sciences University of Pattimura Website: http://matematika.fmipa.unpatti.ac.id
Arjuna Subject : Matematika - Matematika Terapan
Articles 60 Documents
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Search results for , issue "Vol 19 No 3 (2025): BAREKENG: Journal of Mathematics and Its Application" : 60 Documents clear
GEOGRAPHICALLY WEIGHTED GENERALIZED POISSON REGRESSION AND GEOGRAPHICALLY WEIGHTED NEGATIVE BINOMIAL REGRESSION MODELING ON PROPERTY CRIME CASES IN CENTRAL JAVA Arum, Prizka Rismawati; Gautama, Rahmad Putra; Haris, M. Al
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 3 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss3pp1469-1484

Abstract

Property crime in Indonesia remains one of the most prevalent categories of crime across various regions of the country. This category encompasses a range of criminal acts, including theft, illegal appropriation of goods, robbery, motor vehicle theft, arson, and property damage. One of the commonly used regression analysis methods is Poisson regression. The assumption violation of overdispersion in Poisson regression is often found in property crime data in Central Java. This study also considers spatial aspects, depicting local regional characteristics and the integration of local and global variables. Therefore, this study employs Geographically Weighted Generalized Poisson Regression (GWGPR) and Geographically Weighted Negative Binomial Regression (GWNBR) methods with Adaptive Bisquare Kernel weighting. The aim of this research is to develop a model for each district/city in Central Java using Adaptive Bisquare Kernel weighting, thus providing a more accurate representation of the factors influencing property crime in each region. The AIC value criterion of 411.3652 indicates that the GWNBR method is the most suitable for modeling the number of property crime cases in each district/city in Central Java compared to Poisson regression, negative binomial regression, and GWGPR methods.
MODELING GENDER DEVELOPMENT INDEX IN SOUTHEAST SULAWESI PROVINCE USING SEMIPARAMETRIC KERNEL REGRESSION Ampa, Andi Tenri; Laome, Lilis; Ridwan, Muhammad; Baharuddin, Baharuddin; Makkulau, Makkulau
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 3 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss3pp1525-1536

Abstract

The issue of gender equality in Southeast Sulawesi still needs further attention, as indicated by the uneven value of the Gender Development Index (GDI) in each district/city in the region. Therefore, an in-depth analysis is needed to identify factors that affect the GDI. One method that can be used is semiparametric regression with the Nadaraya-Watson estimator, which allows modeling the relationship between variables with more flexibility. This study aims to build a semiparametric regression model to identify factors that contribute to HDI in Southeast Sulawesi Province. The results of the analysis showed that the optimal bandwidth values obtained were h1= 1.57, h2=0.49, h3=2.50 and h4=4.61. The resulting model has an R2 and MSE values of 99.8% and 0.14% respectively, indicating that the model has high accuracy in explaining the overall variation in GDI.
COMBINING FUZZY ANP AND FUZZY ARAS METHODS FOR DETERMINING THE BEST LAND INVESTMENT LOCATION Idris, Chasib; Kurniawaty, Mila; Fitri, Sa`adatul
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 3 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss3pp1499-1512

Abstract

Determining a location for land investment cannot solely rely on intuition, as land investment is one of the economic sectors that frequently changes. Therefore, selecting a land location requires accurate analysis. The purpose of this research is to find the best land investment location using a combination of MCDM (Multi-Criteria Decision Making) methods. The scope of this research focuses on selecting land in Malang City, with the alternatives being all sub-districts in the city. As an initial step, this research employs the Delphi Technique to identify, shortlist, and evaluate the criteria considered by experts in land investment assessment. Six land investment experts participated in this study. The MCDM method used in this research involves two approaches. The weighting of criteria is conducted using the Analytic Network Process (ANP) method, chosen for its ability to account for interrelationships between criteria and alternatives. Following this, the ranking stage utilizes the Additive Ratio Assessment (ARAS) method, which provides utility function values to determine the efficiency of alternatives. To reduce panelist subjectivity, this research uses trapezoidal fuzzy numbers, which are generally better than triangular fuzzy numbers often used in other studies. The assessment results of criteria and sub-criteria indicate that the panelist weightings achieved good hierarchical consistency. From the ANP method combined with the Delphi technique, the Road Access sub-criterion was identified as having the highest weight, followed by the Land Profitability Index sub-criterion, and subsequently by seven other sub-criteria considered in this investment problem. The final outcome of this research, which combines the ANP and ARAS methods with fuzzy usage, shows that the relative efficiency of viable alternatives is directly proportional to the relative impact of the main criteria values and weights considered in the investment. The Arjowinangun sub-district also emerged as the best alternative for land investment.
PRICING OF THE ASIAN OPTION WITH THE KAMRAD-RITCHKEN’S TRINOMIAL MODEL Nabila Wafa’, Jihan; Siswanah, Emy
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 3 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss3pp1457-1468

Abstract

Asian Option determines its payoff option value by the average stock during the option period. This research aims to determine the price of Asian Option by average arithmetic using Kamrad-Ritchken’s Trinomial method. The Kamrad-Ritchken trinomial model is one of the models in the trinomial method used to determine the option value that provides a procedure for determining the barrier parameter or stock price tendency ( ). The stock price tendency makes the trinomial model right on the dotted line of possible stock prices. This study is different from previous studies because the focus of this study is to determine the price of Asian options, both call options and put options with different maturity time variables. The data used for this research are taken from the NVIDIA Corporation (NVDA) data from August 2nd, 2021 – September 29th, 2023. Next, several parameters of option value are determined, which are the initial stock price ( ), contract price ( ), risk-free interest rate ( ), period ( ), stock return ( ), variance ( ), volatility ( ), stock price trend ( ), stock price increase ( ), stock price decrease ( ), stock price increase opportunity ( ), fixed stock price opportunity ( ), stock price decrease opportunity ( ), and barrier ( ). These parameters are used to calculate the price of Asian Option. According to the calculation result by average arithmetic using Kamrad Ritchken’s Trinomial method, the longer the maturity date of an option, the more expensive the option price will be.
OPTIMIZING DEFINED BENEFIT PENSION PLAN FUNDING: COMBINING ENTRY AGE NORMAL METHOD AND SINGLE SALARY APPROACH Ekasasmita, Wahyuni; Rahmi, Nur; Tunnisa, Khaera; Amal, Muhammad Ikhlashul
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 3 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss3pp1553-1564

Abstract

The sustainability of defined benefit pension plans relies heavily on effective funding strategies. This study aims to develop an optimized funding strategy for Defined Benefit Pension Plans by integrating the Entry Age Normal (EAN) method with the Single Salary Approach (SSA). The Entry Age Normal method provides a systematic way to distribute the cost of pension benefits over the career of employees, ensuring long-term stability. Meanwhile, the Single Salary Approach simplifies salary projections, making it easier to manage fund contributions while accounting for future wage inflation. To evaluate the effectiveness of this integrated approach, we conducted a case study using salary and pension fund data collected from internal records at Institut Teknologi Bacharuddin Jusuf Habibie (ITH), a higher education institution. Through a series of simulations and sensitivity analyses, we demonstrate that integrating these methods not only minimizes funding volatility but also improves the accuracy of pension liabilities estimation. For instance, at age 25.83, the actuarial liability is Rp 38,929,501, reflecting a relatively low liability at a younger age. As employees approach retirement, the liability increases significantly. At age 47.17, the liability reaches Rp 191,823,284, demonstrating the impact of salary growth and length of service on future benefits. Additionally, for the same age of 25.83, the actuarial liability under SSA-EAN is Rp 37,980,001, which is slightly lower than the EAN estimate. Pension benefits projected under SSA-EAN are also slightly lower than those under EAN, indicating potential cost savings. The findings provide a viable framework for pension plan administrators seeking to achieve both financial sustainability and predictability in managing pension obligations. By integrating SSA with EAN, this study offers a practical solution that addresses key challenges in the actuarial valuation of defined benefit plans, ensuring more stable and predictable pension funding.
STABILITY ANALYSIS OF GAMBLING BEHAVIOR MODEL WITH COGNITIVE BEHAVIORAL THERAPY TREATMENT Asfa Niswah, Fazat; Nugraheni, Kartika; Fitria, Irma; Dewanti, Retno Wahyu
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 3 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss3pp1879-1892

Abstract

Gambling, driven by the desire for quick profits, involves individuals or groups betting money, often resulting in significant financial consequences. Gambling behavior can be influenced by the environment or society. Thus, the dynamics of environmental influences on gambling behavior can be mathematically modeled using differential equations. This study presents a mathematical model of the environmental impact on the dynamics of the SI1I2T (Susceptible-Infective1-Infective2-Treatment) population of gamblers undergoing cognitive behavioral therapy (CBT). The model replaces the recovered sub-population with a treatment sub-population, representing individuals receiving CBT, as there is no definitive cure for gambling addiction. It consists four sub-populations: It consists of four sub-populations: (S) individuals susceptible to gambling, (I₁) gamblers who are not yet addicted, (I₂) addicted gamblers, and (T) individuals undergoing treatment but at risk of relapse. Mathematical analysis identifies two equilibrium points: a gambling-free equilibrium and an endemic gambling equilibrium. Furthermore, the results of the stability analysis using the linearization method shows that the balance point has a asymptotically stability characteristic requirement. The basic reproduction number ( ) was calculate and resulted if < 1, then the free gambler population equilibrium point is asymptotically stable, and vice versa. Based on the results of the data analysis, the value of = 0.5. This value is less than 1, so the equilibrium point obtained is the free gambler population and asymptotically stable equilibrium point. This means that the population will be free from gambling behavior. Numerical simulation represents the results of the analysis that has been obtained. Providing cognitive behavioral therapy (CBT) to gamblers in treatment can help reduce the gambler population. The population growth will decrease in such a way that it will eventually lead to a gambling-free population
ANALYTICAL APPROACH OF GENERALIZED LINEAR MODELS FOR HANDLING OVERDISPERSION IN POVERTY DATA OF INDONESIA Arisanti, Restu; Pontoh, Resa Septiani; Winarni, Sri; Wibowo, Fellita Odelia; Khairunnisa, Hanifah; Pratama, Raissheva Andika
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 3 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss3pp1575-1586

Abstract

Poverty is one of the complex phenomena that occurs in Indonesia. Various socio-economic variables in Indonesia influence poverty, which we can mathematically model using the Generalized Linear Model (GLM) framework. In this study, we modeled data on the number of poor people per province in 2023 taken from the Badan Pusat Statistik of Indonesia website. The response variable in this study was initially assumed to exhibit equidispersion, where the variance equals the mean. However, the observed variance exceeded the mean, indicating overdispersion. Consequently, Negative Binomial Regression, an extension of the GLM that introduces an additional dispersion parameter, was applied to account for this overdispersion. This approach accommodates overdispersed count data by incorporating a gamma-distributed latent variable. The aim of this study is to determine the best model using Negative Binomial Regression in handling overdispersion in Indonesia's poverty data. This model was chosen for its robustness in capturing increased data variability, enabling the identification of factors that influence poverty. The results of this study offer a mathematically rigorous approach to better understand the underlying dynamics of poverty across provinces in Indonesia.
DERIVATIONS OF PSEUDO BE-ALGEBRAS Indryantika, Nessy; Gemawati, Sri; Kartini, Kartini
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 3 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss3pp1565-1574

Abstract

ESTIMATION OF BENEFIT RESERVES IN ENDOWMENT INSURANCE USING THE INDONESIAN MORTALITY TABLE IV AND ZILLMER METHOD Sadli, Wanda Hamidah; Sari, Devni Prima
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 3 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss3pp1737-1746

Abstract

This study focuses on determining the benefit reserves for endowment life insurance using the Zillmer method, an extension of the prospective reserve approach. Benefit reserves are crucial as they represent the funds insurance companies must set aside to cover future claims. Traditionally, reserves can be calculated retrospectively or prospectively. Still, the Zillmer method introduces an innovative approach by incorporating a Zillmer rate and time to account for loading costs, particularly at the beginning of the policy period. This research's novelty lies in applying the Zillmer method using the most recent Indonesian Mortality Table (TMI) IV, which provides updated and accurate life expectancy data for calculating reserves. The study reveals that the reserve values ​​calculated using the Zillmer method are initially lower than those derived from the conventional prospective method due to the inclusion of the Zillmer rate. However, as the policy progresses, the reserve values ​​gradually align with the prospective reserves after the Zillmer time period concludes. This study not only applies the Zillmer method in a local context with updated mortality data but also demonstrates how insurance companies can manage reserves more effectively, particularly in the early years of the policy.
SPATIAL INTERPOLATION OF RAINFALL INTENSITY IN JAVA ISLAND USING ORDINARY KRIGING Auliyazhafira, Shabira A.; Putri, Fariza A.; Nauli, Theresia S.; Al Madani, Aulia R.; Jaya, I Gede Nyoman Mindra; Falah, Annisa N.; Ruchjana, Budi Nurani
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 3 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss3pp1791-1804

Abstract

Indonesia, situated between two continents and two oceans, experiences a complex climate system influenced by global warming. Climate change has disrupted weather patterns, making it increasingly difficult to predict the rainy and dry seasons and rainfall intensity. However, neighboring regions often exhibit similar weather characteristics, which can be leveraged for prediction. As Indonesia’s economic center, Java Island displays distinct yet interconnected weather patterns, making accurate rainfall prediction crucial for various sectors. This study utilizes 10 years of average rainfall data from NASA’s Power database, covering 64 observation points across Java. Ordinary point kriging is the estimation of a value at a given point and is often used in spatial interpolation analysis in general. Through ordinary point kriging analysis, this study aims to find an accurate kriging equation for predicting rainfall in various regions of Java Island. To achieve this, semivariogram modeling was performed to determine the best theoretical model for spatial interpolation. From 53 sampled regions, 1,378 sample pairs were used to calculate the experimental semivariogram obtained using the R programming language. Next, the theoretical semivariogram was determined using the sill parameter derived from the variance of the sampled data. Three theoretical semivariogram models were considered: spherical, exponential, and Gaussian. The results indicated that the exponential model was the most suitable as it had the smallest SSE value. The results of this analysis enrich our understanding of climate patterns in Indonesia and will contribute to developing mitigation and adaptation strategies related to climate change in the future. The Kriging equation obtained can provide highly accurate prediction results on the test data with a MAPE (Mean Absolute Percentage Error) error measure of 4.85% and RMSE (Root Mean Square Error) of 18.17, which indicates that the prediction results obtained are highly accurate predictions.

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