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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 1,248 Documents
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GROUPING PROVINCES IN INDONESIA BASED ON THE NUMBER OF VILLAGES AFFECTED BY ENVIROMENTAL POLLUTION WITH K-MEDOIDS, FUZZY C-MEANS, AND DBSCAN Syahzaqi, Idrus; Effendi, Magdalena; Rahmawati, Hasri; Kuswanto, Heri; Sediono, Sediono
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 2 (2024): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol18iss2pp0923-0936

Abstract

Pollution can cause the environment to not function properly and ultimately harm humans and other living things. Environmental pollution is a problem that needs to be resolved because it involves the safety, health, and survival of living things. Air pollution in Pekanbaru due to a long dry season has resulted in forest fires. Then, 70% of drinking water is contaminated by fecal waste. In addition, the contamination of the land by the Chevron company resulted in residents suing the company. Until now, there has been no research that has carried out a comparison between methods for grouping villages affected by environmental pollution at the provincial level in Indonesia, so it is important to select the best method for carrying out the grouping. The limitations of this research are the use of three methods for clustering: K-Medoids, Fuzzy C-Means, and DBSCAN. The results showed that Fuzzy C-Means with five clusters have an optimal value compared to DBSCAN with an ICD rate value of 0,351. This method can be used by the government to improve the quality of villages that are clean from pollution in Indonesia, monitoring and evaluation based on the clusters formed.
COMMISSIONERS METHOD FOR LAST SURVIVOR WHOLE LIFE INSURANCE RESERVES WITH GOMPERTZ LAW Hidayat, Agus Sofian Eka; Styven, Arnol
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 2 (2024): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol18iss2pp0937-0948

Abstract

Life insurance plays an important role in protecting one’s life in terms of financial risks. The right required reserve is one aspect that should be secured to obtain a good company’s financial health. A study reported that insufficient reserve is one of the primary causes of insolvency issues among bankrupted insurance companies. Therefore, this study aims to use the Commissioners method in calculating the reserve of the last-survivor whole life insurance policy The Gompertz mortality law is used to estimate Indonesian death probability of age . Gompertz law is employed due to its practical convenience in dealing with continuous case calculation. Linear Least Square Method will be utilized to estimate the Gompertz parameters and . This study uses secondary data from Indonesian Mortality Table IV published by OJK. The result of this study is that the reserve of multiple life status policies, such as last-survivor insurance, depends on the states of individuals of each pair. In this study, the reserve has the highest amount in cases where only the male person is alive. Average Relative Error values of the estimated Gompertz to the TMI IV show that the overall accuracy exhibits a deviation of up to 1.67%. MAPE values of Gompertz show that the estimated model best fits the TMI IV for the interval age of 0-60.
DEVELOPMENT OF SEMIPARAMETRIC PATH ANALYSIS MODELING TRUNCATED SPLINE: DETERMINANTS OF INCREASED REGIONAL ECONOMIC GROWTH Junianto, Fachira Haneinanda; Fernandes, Adji Achmad Rinaldo; Solimun, Solimun; Hamdan, Rosita Binti
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 2 (2024): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol18iss2pp0949-0960

Abstract

This research aims to determine regional economic improvement to achieve a better Indonesian economy and accelerate the path to achieving a Golden Indonesia in 2045 so that it can be realized in a shorter time. This goal will be achieved with the help of statistical analysis methods, where the analysis used in this research is semiparametric truncated spline indirect effect and total effect analysis. The research becomes original in its approach with the utilization of this method and offers novel insights into the dynamics of regional economic development in Indonesia. These methods in this research serve as a tool for analyzing regional economic dynamics, identifying critical factors for improvement, informing policy decisions aimed at realizing Indonesia's economic aspirations for the future, and providing more flexible results to achieve the research objectives. The study was carried out on data with regional expenditure variables as exogenous variables, labor absorption variables as mediating endogenous variables, and regional economic growth variables as pure endogenous variables. The data used in the research are data published by the National/Provincial Central Bureau of Statistics in the form of the Indonesian Statistics Book, BPS publications in the form of Provinces, Provincial Government Financial Statistics, Directorate General of Financial Balance, Sumreg Bappenas, as well as from Ministries, Institutions or Agencies that related to providing data relating to the variables of this research in 2020. The results of this research are that the relationship between regional expenditure variables and labor absorption variables has a significant effect on regional economic growth variables.
MODELING THE INCIDENCE OF MALNUTRITION IN BOGOR REGENCY USING ZERO-INFLATED NEGATIVE BINOMIAL MIXED EFFECT MODEL Sirodj, Dwi Agustin Nuriani; Sadik, Kusman; Kurnia, Anang
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 2 (2024): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol18iss2pp0961-0972

Abstract

Modeling response variables in the form of count data generally uses a model based on the Poisson distribution. However, some conditions, such as the presence of excess zero, can be found in the data that result in overdispersion, which will have an impact on the resulting variance in the model. In this paper, three approaches, namely the Poisson Mixed Model, the Negative Binomial (NB) Mixed Model, and the Zero-Inflated Negative Binomial (ZINB) Mixed Model, are used to model the incidence of malnutrition in Bogor Regency. The data used in this study are secondary data sourced from the West Java open data website. Based on the results of data analysis, it appears that the ZINB Mixed Model method is a method capable of accommodating random effects, overdispersion, and excess zero in modeling malnutrition in Bogor Regency. Variables that significantly affect the occurrence of malnutrition cases in villages in Bogor Regency include the Number of Children Weighed Routinely Every Month, Number of Children Measured for Length and Height Twice a Year, Number of Children under 12 Months Old Who Received Complete Basic Immunization, Number of Posyandu (Integrated Health Post), and Number of Parents/Caregivers Participating in Monthly Parenting (PAUD).
BAYES ESTIMATION OF EXPONENTIALLY DISTRIBUTED SURVIVAL DATA UNDER SYMMETRIC AND ASYMMETRIC LOSS FUNCTIONS Faladiba, Muthia Nadhira; Ahdika, Atina
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 2 (2024): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol18iss2pp0973-0986

Abstract

In a research study, population data are often not available, so the population parameter is unknown. Meanwhile, knowledge about the population parameter is needed to know the characteristics of the studied population. Therefore, it is needed to estimate the parameter of the population which can be estimated by sample data. There are several methods of parameter estimation which are generally classified into classical and Bayesian method. This research studied the Bayesian parameter estimation method to determine the parameters of the exponentially distributed survival data associated with the reliability measure of the estimates under symmetric and asymmetric loss functions for complete sample data in a closed form. The symmetric loss functions used in this research are Squared Error Loss Function (SELF) and Minimum Expected Loss Function (MELF). The asymmetric loss functions used are the General Entropy Loss Function (GELF) and Linex Loss Function (LLF). Performance of some loss functions used in this research are then compared through numerical simulation to select the best loss function in determining the parameter estimation of the exponentially distributed survival data. We also studied which loss function is best for underestimation and overestimation modeling. Based on simulation results, the Bayes estimates using MELF is the best method to estimate population parameters of the exponentially distributed survival data for the overestimation modeling, while LLF is the best for the underestimation modeling. We provided direct application in a case study of fluorescence lamp survival data. The results show that the best method to estimate the parameter of the standard fluorescence life data is using LLF for underestimation with and MELF for overestimation with .
APPLICATION OF COX PROPORTIONAL HAZARD REGRESSION FOR ANALYZING FACTORS INFLUENCING THE RECOVERY RATE OF PULMONARY TUBERCULOSIS PATIENTS Irfanullah, Asrul; Damamain, Ferina Lestari; Tuanaya, Nur Amaliya
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 2 (2024): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol18iss2pp0987-0996

Abstract

Pulmonary tuberculosis is a serious disease that requires special attention from the community and the Government of Indonesia, especially the Maluku Province. One commonly used analytical method in the health field is survival analysis. Survival analysis is a statistical method related to observing the period until the occurrence of an event or events. This study aims to model and identify factors that affect the recovery rate of patients with pulmonary tuberculosis in Ambon City using Cox Proportional Hazard regression. The results of the Hazard Ratio interpretation show that the variables that have a significant influence are chest pain and night sweats. Specifically, patients experiencing chest pain exhibit a recovery rate 0.487264 times faster than those devoid of such symptoms. Similarly, patients experiencing night sweats demonstrate a recovery rate of 0.619839 times faster than their counterparts not experiencing this symptom. This study highlights the imperative of recognizing and addressing symptoms like chest pain and night sweats in managing pulmonary tuberculosis in Ambon City.
NATIONAL HEALTH INSURANCE AND CATASTROPHIC HEALTH EXPENDITURE: A COMPLEMENTARY LOG-LOG APPROACH ON YOGYAKARTA’S INCIDENCE 2022 Fakhriandi, Erdi; Sofa, Wahyuni Andriana
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 2 (2024): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol18iss2pp0997-1008

Abstract

National Health Insurance (JKN) aims to provide health care benefits to meet people's basic health needs. However, despite the high JKN coverage in D.I.Yogyakarta Province, catastrophic health expenditure events remain high. The study examines the implementation of National Health Insurance (JKN) in D.I.Yogyakarta Province and its effectiveness in reducing devastating health expenditures in 2022. Using the Complementary Log-log approach on the 2022 National Social and Economic Survey data, the research findings reveal that the implementation of JKN has been successful, and the ownership of JKN positively affects the reduction of catastrophic health expenditure. The study also shows that the education level of household members and household size have positive effects on reducing the incidence of catastrophic health expenditures. However, the presence of babies or the elderly, household economic status, and inpatient status could increase the risk of having catastrophic health expenditures. The study highlights the need for attention to be given to implementing JKN in D.I.Yogyakarta Province and other variables to achieve universal health coverage and reduce catastrophic health expenditure.
TWOFOLD SUBAREA MODEL FOR ESTIMATING COMMUTER PROPORTION IN 10 METROPOLITAN AREAS Amin, Yudi Fathul; Indahwati, Indahwati; Kurnia, Anang
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 2 (2024): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol18iss2pp1009-1022

Abstract

The metropolitan area is a major contributor to national GDP. The metropolitan area is a center of attraction for many people who come to earn income as commuters. Commuters are people who carry out work activities in the center of the metropolitan area, which are carried out by residents who live in suburban areas around the center of the metropolitan area and commute regularly every day. The availability of commuter statistics from surveys for presentation level down to the smallest administrative level, such as regencies/municipalities, is unreliable. This happens because this level of presentation has poor precision due to insufficient samples due to the Statistics Indonesia survey design for making estimates at the national and provincial levels. It can be done using small area estimation (SAE) to meet increasing data needs, but existing SAE models can often estimate only at one level. To meet data requests more effectively, a model is needed that can estimate several small areas simultaneously. In SAE, one of the SAE models that can do this is the twofold subarea model. The twofold subarea model produces estimates of the proportion of commuters with good precision at the subarea level (regencies/municipalities) and area level (metropolitan area), with the RRMSE percentage value of the estimated proportion of commuters being below 25% for all regions. The results of this research can be used to present commuter data at the regencies/municipalities level and metropolitan area level where there is a lack of samples and become a new opportunity for Statistics Indonesia to increase statistical production in small areas, which is more effective compared to other SAE methods which have so far been used only to estimate one area level.
ON THE MOMENTS OF THE 3-PARAMETER GOMPERTZ DISTRIBUTION Hakiki, Moch Taufik; Adipradana, Dimaz Wisnu; Ahmad, Imam Safawi; Putri, Lahfanda Dista Permata
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 2 (2024): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol18iss2pp1023-1036

Abstract

Gompertz distribution is a classical probability distribution extensively used in actuarial science, reliability, and survival analysis. Gompertz distribution also plays a role in various fields, such as biology, economics, and marketing analysis. Some extensions of this distribution have been studied and applied to various problems. In this article, we are concerned with some statistical properties of a 3-parameter Gompertz distribution. This extension of the Gompertz distribution introduced has been used in studying competing risk survival analysis. Our main results are the derivation of moments of this distribution and other statistical properties related to moments, such as moment generating function, mean residual life function, mean inactivity time and Lorenz curve. These results will serve as a complement to the theoretical aspect of the analysis of the distribution.
MATHEMATICAL MODEL OF REPELLENT EFFECT IN DENGUE TRANSMISSION Handayani, Dewi; Gunadi, Audri Utami; Rachmawati, Ria Nurlita
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 2 (2024): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol18iss2pp1037-1052

Abstract

Dengue is a disease caused by the dengue virus, transmitted through the bite of an infected female Aedes aegypti. Dengue virus is a member of the genus Flavivirus, family Flaviviridae. Indonesia is one of the countries with the most dengue cases in Southeast Asia. Therefore, dengue transmission must be controlled to reduce the increase in dengue cases. One of the controls is by using repellents. Repellent is one of the human protection strategies to avoid mosquito bites used by spraying or smearing. This study models dengue transmission by reviewing the effect and control of repellent. A mathematical model of repellent effect and control in dengue transmission uses a SIR compartment model. The SIR model is modified by involving mosquitoes and the human population. Repellent is used in both susceptible humans, infected humans, and recovered humans. Numerical and analytical simulations are conducted to analyze the behavior of each compartment of the mosquito and human populations in dengue transmission. Analytical results show that the factors affecting the spread of infection are the transmission rate of the dengue virus and the loss of human-repellent protection. The transmission rate of dengue virus in the interval increases the infected human by 2.73%, while the rate of loss of human repellent protection in the interval increases the infected human by 0.03%. Optimal control is used to minimize the number of infected humans who do not use repellent. The results of numerical simulations on the optimal control problem show that an increase in the proportion of healthy humans who have campaign effect and use repellent regularly in the range of 14.67% can reduce infected individuals by 0.647%.

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