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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 1,429 Documents
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COMPARING STATISTICAL AND DEEP LEARNING METHODS FOR INSURANCE CLAIM ESTIMATION: A CASE STUDY OF HIDDEN MARKOV MODEL (HMM) AND CONVOLUTIONAL NEURAL NETWORK - LONG SHORTTERM MEMORY (CNN-LSTM) Ainun Mawaddah Abdal; Andi Muhammad Anwar; Illuminata Wynnie; Amil Siddik; Edy Saputra Rusdi; Mauliddin Mauliddin
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 4 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss4pp2711-2726

Abstract

The insurance industry relies heavily on accurate claim prediction to support risk management, reserve allocation, and financial stability. However, motor vehicle insurance claim data are typically characterized by temporal dependency, highly skewed distributions, and fluctuating claim severity, making accurate prediction a challenging task. While deep learning approaches have recently gained attention for time-series forecasting, their effectiveness on moderate-scale insurance claim datasets remains uncertain. This study aims to compare the predictive performance of the Hidden Markov Model (HMM) and CNN-LSTM in modelling temporal patterns and predicting daily motor vehicle insurance claims. In addition, an Attention-LSTM + XGBoost ensemble model is included as a supplementary deep learning benchmark. This study utilizes historical motor vehicle insurance claim data collected from 2017 to 2021, consisting of 11,679 claim observations. The data preprocessing stage included data cleaning, missing value handling, outlier detection, and claim severity categorization for HMM modelling. The HMM parameters were estimated using the Baum–Welch algorithm, while the deep learning models were trained using sequential claim data. Model performance was evaluated using Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), and coefficient of determination (R^2) on the testing dataset to ensure objective comparison. The experimental results show that the HMM model achieved the best predictive performance, outperforming both the CNN-LSTM and Attention-LSTM + XGBoost models. The findings indicate that the probabilistic structure of HMM is more suitable for modelling the temporal risk patterns and fluctuating claim behavior observed in the motor vehicle insurance dataset. Furthermore, the study demonstrates that classical probabilistic models can remain competitive and even outperform more complex deep learning approaches when applied to moderately sized insurance claim datasets with limited hidden complexity.
WHEAT PRICE PREDICTION USING PULSE FUNCTION INTERVENTION ANALYSIS APPROACH Sediono Sediono; Nuzulia Anida; Nabila Angel Nafisha
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 4 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss4pp2727-2742

Abstract

This study examines the impact of the Russia–Ukraine conflict on international wheat prices and develops a short-term forecasting model using intervention analysis. The study addresses a gap in the existing literature by applying a pulse-function intervention to capture sudden price shocks from geopolitical events, which are often inadequately modeled in conventional time-series approaches. Monthly wheat price data from January 2020 to November 2022 were analyzed using an intervention model combined with an ARIMA framework. The results indicate a statistically significant price spike following the onset of the conflict, confirming the presence of a short-term shock effect. The best-fitting model, ARIMA(0,2,1), produced an Akaike Information Criterion (AIC) value of -2097.84 and a Mean Squared Error (MSE) of 47,632.17, indicating satisfactory predictive performance for short-term forecasting. This study contributes methodologically by integrating pulse intervention analysis with ARIMA modeling to better capture abrupt disruptions in commodity prices. The findings provide empirical evidence of the sensitivity of global wheat markets to geopolitical instability and offer policymakers insights for designing responsive food security strategies. However, this study is limited by its relatively short observation period and by the exclusion of external variables, such as energy prices and trade policies, which may also influence price dynamics.
BIFRAMES AND THEIR PROPERTIES IN QUATERNIONIC HILBERT SPACES Nitin Sharma; Amita Aggarwal; Raksha Sharma
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 4 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss4pp2743-2754

Abstract

In this paper, we focus on defining and analyzing biframes within quaternionic Hilbert spaces, thereby extending the study of biframes beyond the complex Hilbert space framework. We establish that frames can be viewed as a specific instance of biframes. Moreover, we introduce the concept of biframe operators and utilize it to derive a reconstruction formula. Several characterization results pertaining to biframes are also discussed. Additionally, the conditions under which the image of a biframe under a bounded linear operator continues to retain the biframe structure are examined.
SURVIVAL TIME MODELING IN HEMODIALYSIS PATIENTS USING A WEIBULL MIXTURE PROPORTIONAL HAZARDS MODEL Rahida Rihhadatul Aisy; Nur Iriawan; Shofi Andari; Mayta Rithmala; Yani Sumartin
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 4 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss4pp2755-2768

Abstract

Hemodialysis is a critical treatment for patients with end-stage chronic kidney disease (CKD). Although it is associated with a higher risk of mortality and complications compared to other renal treatment choices, many patients prefer hemodialysis as their renal replacement therapy. Traditional parametric survival models often struggle to capture the complexity of the distribution due to multimodal survival data in heterogeneous populations, such as hemodialysis patients. To overcome this, mixture models provide greater flexibility by combining several distributions to better reflect latent survival patterns. This study investigates mortality risk factors by applying a Bayesian Weibull mixture proportional hazards model to 151 hemodialysis patients from one hospital in Surabaya, Indonesia, in 2024, with data extracted from medical hospital records. The Expectation-Maximization and No-U-Turn Sampler (EM-NUTS) approach was used to estimate model parameters and latent class memberships. The Expectation-Maximization (EM) approach, originally developed for control charts and time series, was adapted for survival analysis to address latent heterogeneity. Exploratory analysis reveals multimodal survival distributions, suggesting distinct risk groups. Model selection using the Bayesian Information Criterion and the Akaike Information Criterion identified two latent groups with distinct risk profiles. In the first group, male gender and diabetes significantly increased mortality risk, while hypertension had a smaller effect. In the second group, hypertension was the dominant risk factor, with less influence from gender and diabetes. These findings emphasize the importance of accounting for population heterogeneity in the survival analysis of hemodialysis patients. The use of advanced Bayesian mixture models with EM-NUTS estimation provides robust tools for uncovering hidden subgroups and improving risk stratification, allowing for more personalized treatment strategies in CKD care.
A NEW ONE-PARAMETER DISTRIBUTION FOR MODELING POSITIVE SKEWNESS DATA: THE GENERIC KRISON DISTRIBUTION Elbert Krison; Siti Nurrohmah; Sindy Devila; Ida Fithriani
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 4 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss4pp2769-2782

Abstract

Inspired by the hyperbolic secant distribution and a specific hyperbolic trigonometric identity, we propose a new continuous distribution with one parameter, called the Generic Krison distribution. We derive its probability density function, survival function, cumulative distribution function, hazard function, quantile function, and mean excess loss function. Closed‑form expressions for the moment generating function are also provided. Statistical measures including the raw moments, mean, variance, standard deviation, median, mode, skewness, kurtosis, coefficient of variation, and index of dispersion are obtained. The distribution exhibits constant moderate positive skewness and a constant coefficient of variation, making it a natural candidate for modeling positively skewed data. The parameter is estimated by the method of maximum likelihood; because the score equation is transcendental, the estimate is obtained numerically. We compare the Generic Krison distribution with the one‑parameter Rayleigh, Lindley, and Bilal distributions across three datasets (income, survival time, mortality rate). The results demonstrate that the Generic Krison distribution performs well on all three datasets, offering a promising new tool for statistical modeling.
A HYBRID ARIMA-DISCRETE WAVELET TRANSFORM MODEL FOR ENHANCED COASTAL SEA LEVEL FORECASTING Hakami Ali Mohammed; Muhammad Fadhil Marsani; Mohd Shareduwan Mohd Kasihmuddin; Farid Zamani Che Rose; Basri Badyalina
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 4 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss4pp2783-2798

Abstract

Accurate sea level forecasting is essential for coastal resilience, as rising sea levels threaten coastal residents, infrastructure, and ecosystems, heightening the hazards of floods and erosion; yet, conventional models struggle with non-linear trends. This study proposes a hybrid ARIMA-DWT (Autoregressive Integrated Moving Average with Discrete Wavelet Transform) model to enhance prediction accuracy by decomposing sea level data into linear (ARIMA) and non-linear (DWT) components. The hybrid model, utilizing monthly sea level data from Penang, Malaysia (1984–2018; N=408), diminished errors by 20% compared to the standalone ARIMA, attaining out-of-sample RMSE=81.76, MAE=68.40, and MAPE=2.45%. The ARIMA-DWT framework effectively captures long-term climate trends and short-term variations, providing a computationally efficient resource for coastal planners. This method demonstrates enhanced efficacy in situations characterized by significant seasonality, offering practical insights for climate adaptation. This research enhances the existing body of work on hybrid forecasting techniques by providing a scalable framework for areas vulnerable to sea level rise.
PREDICTING HOURLY AMBULANCE USAGE FOR TWO SELECTED GOVERNMENT HOSPITALS IN MALAYSIA; COMPARISON BETWEEN SEASONAL AUTOREGRESSIVE INTEGRATED MOVING AVERAGE (SARIMA) AND SEASONAL DECOMPOSITION MODELS Loshini Thiruchelvam; Nur Balqishanis Zainal Abidin; Uma Eswari Punchanathan; Nur Dayana Abdul Rahman; Nur Amalina Mat Jan; Jane Irene P. J. Antony
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 4 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss4pp2799-2812

Abstract

An ambulance is a vehicle used to transport sick or injured people, and the patient will be sent to a hospital for further treatment. This study aims to predict hourly use of ambulances in two selected government hospital, namely the Hospital Sultanah Nur Zahirah (HSNZ), located in Terengganu, a state in the East Peninsular Malaysia, and Hospital Tapah, located in Perak state, in the West Peninsular Malaysia. Data on hourly ambulance usage were obtained from the hospital’s emergency department for 2010. Two distinct statistical models, namely the Seasonal Autoregressive Integrated Moving Average (SARIMA) and Seasonal Decomposition model, were used to model the dataset. The study found that both hospitals have different best forecasting models: HSNZ uses the Seasonal Decomposition Model, whereas the SARIMA model was found to forecast better at Hospital Tapah. For example, in the HSNZ study, the study determined the best SARIMA model from a few candidate models, namely. This model showed good performance on the training dataset and performed best on the test dataset. However, when further compared with the seasonal decomposition model, the study found the latter model to perform better. When visually investigated as well, the model’s forecasted values were close to the actual values, or at least relatively acceptable. So far, this study concludes that the developed model is highly localized and specific to the given dataset.
EXPLICIT MEAN PARAMETERIZATION AND BHHH-BASED ESTIMATION IN THE PGIG REGRESSION MODEL Yusrianti Hanike; Purhadi Purhadi; Achmad Choiruddin
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 4 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss4pp2813-2824

Abstract

Modeling dispersed count data remains a substantial challenge in applied research, especially when traditional models struggle to capture complex dispersion structures or yield interpretable results. In this study, we introduce and evaluate the Poisson Generalized Inverse Gaussian Regression (PGIGR) model, which offers a flexible four-parameter framework with explicit mean parameterization. The model is applied to 2023 maternal mortality data from 38 cities and municipalities in East Java, Indonesia. The response variable was the number of maternal deaths, while the six predictors were the percentage of pregnant women receiving nutritional tablets, the percentage of malnourished pregnant women, contraceptive use, antenatal care coverage, healthcare professional availability, and access to proper sanitation. The results indicate that higher nutritional tablet coverage among pregnant women and greater antenatal care coverage are significantly associated with lower maternal mortality. In contrast, higher percentages of malnourished pregnant women, contraceptive users, healthcare professionals, and households with access to proper sanitation are significantly associated with higher maternal mortality. The unexpected positive associations observed for contraceptive use, healthcare professional availability, and proper sanitation may reflect differences in regional health needs, service allocation, reporting practices, or other unobserved factors and therefore require further investigation. Goodness-of-fit testing confirms the suitability of the PGIGR model for the data, and the maximum likelihood estimation procedure—supported by the BHHH optimization algorithm—yields statistically significant parameter estimates. This research underlines the applicability of the PGIGR model for modeling count data characterized by dispersion, while maintaining interpretability of the regression parameters. Such a framework can support informed decision-making in public health management and the strategic allocation of healthcare resources. The data on maternal mortality were obtained from the 2023 Health Profile of East Java Province, published by the East Java Provincial Health Office.
INTEGRATION OF QUADRATIC REGRESSION-ARIMA MODEL ESTIMATING AIR QUALITY INDEX ON PM2.5 CONCENTRATION Tiara Herlinda Sari; Yundari Yundari; Shantika Martha
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 4 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss4pp2825-2838

Abstract

In Air Quality Index (AQI) computation, the relationship between AQI and PM2.5 is defined through an interpolation approach, which forms a nonlinear relationship between PM2.5 and AQI, thereby rendering linear regression less capable of representing this relationship. This research selects quadratic regression because it explicitly represents the nonlinear relationship between PM2.5 and AQI while remaining easy to interpret and minimizing the risk of overfitting compared with more complex nonlinear models. However, in time series data, this model still generates residuals that violate classical assumptions due to time dependence. Hence, a hybrid modeling approach integrates quadratic regression and Autoregressive Integrated Moving Average (ARIMA) to represent nonlinear relationships while correcting the time dependence on the quadratic regression residuals. This research aims to estimate AQI based on PM2.5 in Pontianak in 2024 using the Quadratic Regression-ARIMA model, also comparing the performance of quadratic regression models and quadratic regression-ARIMA models. This research focuses on estimation and interpolation within the sample, not forecasting. The dataset consists of 366 daily observations of AQI and PM2.5 throughout 2024, obtained from the official air quality monitoring website, AQI. The analysis was carried out by estimating the AQI from PM2.5 using a Quadratic Regression model, and the regression residuals were rendered stationary before ARIMA modeling. The results showed that the Quadratic Regression-ARIMA model yields estimate with a better residual structure than the quadratic regression model. The in-sample evaluation of the Quadratic Regression-ARIMA model showed better performance, with a higher coefficient of determination of 0.95, compared with 0.91 for quadratic regression and 0.80 for linear regression.
INTEGRATING STRUCTURED AND UNSTRUCTURED FEATURES FOR E-TICKETING CLASSIFICATION: A MACHINE LEARNING AND ENSEMBLE-BASED APPROACH Siti Zulaikha Mohd Jamaludin; Majid Khan Majahar Ali; Eric Wong Vun Shiung; Mohd Tahir Ismail; Noor Farizah Ibrahim; Nur Ezlin Zamri
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 4 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss4pp2839-2850

Abstract

E-ticketing systems (ETS) generate mixed information from categorical ticket attributes and free-text descriptions, yet many classification studies still treat these sources separately, which can limit routing accuracy. This study aims (i) to develop an effective preprocessing pipeline for hybrid data, (ii) to develop a two-stage feature selection (2-FS) pipeline for hybrid data, (iii) to design an ensemble classification framework that improves hybrid data performance, and (iv) to benchmark all implemented and proposed models using real-world ETS data. The methodology builds a unified preprocessing workflow by combining Natural Language Processing for textual feature with categorical encoding for categorical features, followed by feature concatenation and vector-space integration to form hybrid representations. Five baseline classifiers (LR, SVM, MNB, RF, and KNN) are evaluated and extended with majority-vote ensembles that pair LR with other classifiers (LR-S, LR-M, LR-R, LR-K, and LR-ALL). Model performance is assessed using accuracy, precision, recall, and F1-score, and the Friedman test is applied to examine statistical consistency across datasets. Results show that hybrid data consistently outperforms single-type datasets, while categorical-only data yields the lowest scores. The best hybrid ensemble of LR-K achieves up to 93% classification accuracy, with strong overall performance also observed for RF on hybrid data. The Friedman test indicates minimal rank differences across models, suggesting that several classifiers are competitive under this ETS setting. Limitations include possible noise and overfitting effects that reduce separation between dataset types. Future work will explore feature ranking-based selection, data-driven segmentation during preprocessing, multi-level classification, imbalance handling, and deeper ensemble strategies to strengthen robustness and generalization.

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