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Jambura Journal of Mathematics
Published by Universitas Negeri Gorontalo
ISSN : 26545616     EISSN : 26561344     DOI : https://doi.org/10.34312/jjom
Core Subject : Education,
Mathematics
Jambura Journal of Mathematics (JJoM) is a peer-reviewed journal published by Department of Mathematics, State University of Gorontalo. This journal is available in print and online and highly respects the publication ethic and avoids any type of plagiarism. JJoM is intended as a communication forum for mathematicians and other scientists from many practitioners who use mathematics in research. The scope of the articles published in this journal deal with a broad range of topics, including: Mathematics; Applied Mathematics; Statistics; Applied Statistics.
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Articles 16 Documents
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Search results for , issue "Vol 7, No 2: August 2025" : 16 Documents clear
Parameter Estimation and Hypothesis Testing of GTW Compound Correlated Bivariate Poisson Regression Model: A Theoretical Development Hargandi, Priyanka Ratulangi; Purhadi, Purhadi; Choiruddin, Achmad
Jambura Journal of Mathematics Vol 7, No 2: August 2025
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v7i2.32712

Abstract

Each observation location and time possesses distinct characteristics, reflecting heterogeneity at every observation point, both spatially and temporally. This condition renders the Compound Correlated Bivariate Poisson Regression (CCBPR) model inadequate for representing data dynamics that exhibit spatial and temporal heterogeneity. To address this limitation, the Geographically and Temporally Weighted Compound Correlated Bivariate Poisson Regression (GTWCCBPR) model is employed, which allows parameter variation across locations and time periods. This model also incorporates the exposure variable as a weighting factor to adjust for differences in risk across observational units. This study aims to estimate the parameters of the GTWCCBPR model using the Maximum Likelihood Estimation (MLE) approach. Due to the complex structure of the model, the log-likelihood function does not yield a closed-form solution. Therefore, parameter estimation is performed using the iterative Berndt-Hall-Hall-Hausman (BHHH) algorithm. Subsequently, hypothesis testing is conducted to evaluate the parameter similarity between the global model (CCBPR) and the spatiotemporal model (GTWCCBPR), as well as to assess the significance of each predictor variable. Simultaneous testing is carried out using the Maximum Likelihood Ratio Test (MLRT), while partial testing is conducted using the Z-test. The scope of this study is limited to theoretical formulation and methodological development, without empirical or simulation-based validation. Future research may extend this work by applying the GTWCCBPR model to practical datasets exhibiting spatio-temporal heterogeneity, particularly in areas such as public health (e.g., maternal and postneonatal mortality), epidemiology, or regional planning.
Estimasi Premi Bruto Asuransi Kendaraan Bermotor Menggunakan Metode Panjer Recursion dan Fast Fourier Transform Nugrahainy, Sintya Putri; Azizah, Azizah
Jambura Journal of Mathematics Vol 7, No 2: August 2025
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v7i2.32280

Abstract

Insurance is an agreement between two parties, namely the insurance company as the insurer and the customer as the insured. In practice, an insurance product can have hundreds or even thousands of policy contracts. This condition requires the insurer to model the compound distribution of total aggregate loss, which involves repeated convolutions. However, applying convolution to a large number of policies becomes increasingly difficult and inefficient. Therefore, alternative methods are needed to optimize the calculation process. This study uses the Panjer Recursion and Fast Fourier Transform methods to approximate the aggregate loss distribution. The model applies the Zero-Truncated Negative Binomial distribution for claim frequency and the Burr distribution for claim severity. The results show that Panjer Recursion and Fast Fourier Transform yield the same values, resulting in identical probability distributions for all values of aggregate loss. The aggregate loss distribution is then used to estimate gross premium based on the pure premium principle and the expected value principle. The loading factors increase as the confidence level rises, with θ = 3.51 at the 95% confidence level and θ = 5.47 at the 99% confidence level, resulting in total gross premiums of IDR 109,510,000 and IDR 520,835,000, respectively. The choice of confidence level plays a strategic role for insurance companies in balancing risk protection with premium affordability.
Evaluation of the SARIMA and Prophet Models in Forecasting Ship Passenger Numbers at Balikpapan Port Cintani, Meavi; Nizar, Yeky Abil; Angraini, Yenni; Notodiputro, Khairil Anwar; Mualifah, Laily Nissa Atul
Jambura Journal of Mathematics Vol 7, No 2: August 2025
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v7i2.31606

Abstract

Balikpapan Port serves as a vital transportation hub in eastern Indonesia, particularly in supporting the development of the Nusantara Capital City (IKN). This study evaluates the performance of Seasonal Autoregressive Integrated Moving Average (SARIMA) and Prophet models in predicting short-term ship passenger volumes using monthly data from January 2006 to December 2024 obtained from the East Kalimantan Provincial Transportation Office. Our analysis identifies SARIMA (MAPE = 24%) as the more accurate model compared to Prophet (MAPE = 34%). The optimal SARIMA model was then used to generate a focused forecast for December 2025, providing targeted insights for peak-season port management. These results assist port authorities in resource allocation, infrastructure planning, and policy formulation to accommodate anticipated passenger surges during critical periods.
Parameter Estimation of Mixed Geographically Weighted Bivariate Zero-Inflated Negative Binomial Regression Model Islamiati, Mawadah Putri; Purhadi, Purhadi; Wibawati, Wibawati
Jambura Journal of Mathematics Vol 7, No 2: August 2025
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v7i2.32711

Abstract

The Bivariate Zero-Inflated Negative Binomial (BZINBR) regression model is commonly used to analyze two correlated count response variables characterized by overdispersion and excess zeros. To account for spatial heterogeneity in predictor effects, the BZINBR model has been extended into the Geographically Weighted BZINBR (GWBZINBR) model. However, predictor effects are not always entirely local; certain global effects may persist across regions. This study proposes the Mixed Geographically Weighted BZINBR (MGWBZINBR) model, which integrates both global and local parameter structures for modeling spatially correlated bivariate count data. The theoretical framework of the MGWBZINBR model is developed, including the derivation of the log-likelihood function, parameter estimation procedures, and hypothesis testing. Parameter estimation is conducted using the Maximum Likelihood Estimation (MLE) method via the iterative Berndt–Hall–Hall–Hausman (BHHH) algorithm. Given the complexity of the likelihood equations and the absence of closed-form solutions, numerical optimization is employed to ensure convergence and stability. The MGWBZINBR model offers a flexible and robust framework for analyzing spatial count data with excess zeros and complex dependency structures. It can be applied in various fields, including public health, ecology, and transportation analysis, to understand the influence of both local and global predictors on spatial phenomena. As the focus of this paper is methodological, empirical and simulation-based applications are intentionally excluded.
Conditional Value at Risk Portfolio With Monte Carlo Control Variates Maga, Fahmi Giovani; Sulistianingsih, Evy; Satyahadewi, Neva
Jambura Journal of Mathematics Vol 7, No 2: August 2025
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v7i2.30952

Abstract

Stock investment is one of the instruments investors favor due to its potential for high returns, but the risks stemming from stock price volatility cannot be overlooked. Value at Risk (VaR) is commonly used as a standard approach to measure and manage these risks. However, VaR has limitations in handling extreme risks, making Conditional Value at Risk (CVaR) is a more effective choice. This research measures the application of CVaR to a portfolio of banking sector stocks in Indonesia using the Monte Carlo Control Variates (MCCV) technique, with the Indonesia Composite Index (ICI) as the control variable. The portfolio consists of stock of PT Bank Rakyat Indonesia Tbk (BBRI) and PT Bank Negara Indonesia Tbk (BBNI). The purpose of this research is to compare CVaR calculation results using Standard Monte Carlo Simulation (MCS) and MCCV simulations. The data used includes the daily closing prices of BBRI, BBNI, and ICI stocks for the period from March 1, 2023, to February 29, 2024. The VaR and CVaR calculated in this study are for one day. The results of the analysis show that the MCS CVaR values at 90%, 95%, and 99% confidence levels are 1.730%, 2.050%, and 2.569%, respectively, while the MCCV CVaR values at 90%, 95%, and 99% confidence levels are 1.400%, 1.662%, and 2.084%, respectively. These values indicate that using the ICI as a control variable has successfully improved risk estimation by utilizing the ICI as a control variable.
Pemodelan Deret Waktu Menggunakan Non-linear Autoregressive Neural Network: Studi Kasus Prediksi Harga Saham Mandiri Najib, Mohamad Khoirun; Nurdiati, Sri
Jambura Journal of Mathematics Vol 7, No 2: August 2025
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v7i2.33397

Abstract

Accurate stock price forecasting is critical for investment decision-making, yet the nonlinear and complex nature of time series data poses significant challenges. This study investigates the application of the Nonlinear Autoregressive Neural Network (NARNN) for modeling the monthly stock price time series of PT Bank Mandiri (Persero) Tbk (BMRI) from January 2011 to December 2023. The model is constructed by exploring combinations of feedback delays and hidden neurons to identify the optimal configuration based on the root mean squared error. The dataset is divided into training, validation, and testing. Evaluation results show that the configurations 8–12 and 8–13 yield the best testing accuracy with a MAPE of 4.71%. An ensemble mean strategy is also employed, producing competitive and stable performance. These findings demonstrate that the NARNN approach effectively captures nonlinear patterns in stock data and holds promise for financial forecasting applications.
Dynamical Analysis of Online Shopping with Beauty Influencer Andani, Meri Teri; Zulaikha, Zulaikha
Jambura Journal of Mathematics Vol 7, No 2: August 2025
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v7i2.33363

Abstract

This study develops a modified nonlinear mathematical model of online shopping dynamics that explicitly incorporates the direct influence of beauty influencers through promotional content (F) and a parameter α for transition from offline to online shopping without the influence of influencers. The model comprises offline shoppers (L), online shoppers (O), and the amount of promotional content created by beauty influencers (F). Stability analysis shows two equilibrium points: an online shopping-free state E1 locally asymptotically stable when R0 1 and an endemic state E2 locally asymptotically stable when R0 1. Numerical simulations using MATLAB R2013a confirm the analysis, revealing that higher promotional content growth rates (k) and lower decline rates (θ) increase R0 and the online shoppers population. The novelty lies in explicitly modeling influencer-based promotional content as a driver of shopping behavior, offering strategic insights for sustained engagement and customer retention in beauty sector digital marketing.
Model Matematika Penyebaran Penyakit Demam Berdarah Dengue dengan Faktor Kesadaran Sosial: Analisis dan Simulasi Djuma, Clara Anggriani; Achmad, Novianita; Nuha, Agusyarif Rezka; Hasan, Isran K.; Arsal, Armayani
Jambura Journal of Mathematics Vol 7, No 2: August 2025
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v7i2.33921

Abstract

Dengue haemorrhagic fever (DHF) is a serious health problem in many tropical regions, including Indonesia. The spread of this disease is influenced by various factors, one of which is the level of social awareness in the prevention and control of infection. This study developed a mathematical model of DHF spread by integrating social awareness as an additional compartment. The model was analysed by determining the equilibrium points and the basic reproduction number (R0), as well as stability analysis using the Routh–Hurwitz criterion. The analysis results show the existence of two types of equilibrium points: the disease-free equilibrium point (T1) and the endemic equilibrium point (T2). Point T1 is locally asymptotically stable when R0 1 and unstable when R0 1, while point T2 is locally asymptotically stable when R0 1. Sensitivity analysis shows that the social awareness parameter significantly influences the value of R0. Additionally, numerical simulations indicate that increasing social awareness can effectively reduce disease spread and drive the system toward a disease-free state. These findings underscore the importance of community-based awareness interventions in dengue control strategies.
Predator-Prey Dynamics in the Interaction of HIV Virus with CD4+T Cells Andika, Fadly; Sukarsih, Icih
Jambura Journal of Mathematics Vol 7, No 2: August 2025
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v7i2.33911

Abstract

This study analyzes the interaction dynamics between the human immunodeficiency virus (HIV) and CD4+T cells using a predator–prey mathematical model, in which HIV is represented as the predator and CD4+T cells as the prey. The model aims to describe the long-term behavior of the immune system when challenged by the virus. Analytical results show that the system has two equilibrium points: a disease-free equilibrium E1 and an endemic equilibrium E2, whose explicit forms are derived in closed form. Stability analyses of both the disease-free and endemic states are conducted through system linearization, Jacobian matrix formulation, and application of the Routh–Hurwitz criteria. The disease-free state is found to be locally asymptotically stable when the viral elimination rate by the immune system exceeds a specific threshold determined by the balance between viral infection and CD4+T cell production, indicating that under certain conditions the immune system can suppress the virus naturally. The endemic state, representing chronic infection, is stable when the combined effects of viral replication and immune response surpass the rate at which healthy CD4+T cells are lost, implying that the virus can persist within the host. Numerical simulations in Python, using parameter values from previous studies, confirm the coexistence of the virus and host cells under specific conditions. The findings emphasize the influence of viral replication and immune response rates on system stability, offering insights into how HIV can maintain chronic infection without completely depleting CD4+T cells.
A Comparative Study of Linear and Quadratic Spline Regression Models for Predicting HbA1c Levels in Patients with Diabetes Mellitus Arifin, Samsul; Anggraini, Dewi; Salam, Nur
Jambura Journal of Mathematics Vol 7, No 2: August 2025
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v7i2.33292

Abstract

HbA1c is widely recognized as a key clinical indicator for monitoring and controlling diabetes, as it reflects average blood glucose levels over the preceding 2–3 months and is closely linked to the risk of complications. This study compares linear and quadratic truncated spline regression models for predicting HbA1c levels in patients with diabetes mellitus. The analysis used retrospective medical record data from a hospital in Makassar, Indonesia, collected in 2023. Fasting blood glucose and LDL cholesterol were included as predictors, with HbA1c as the response variable. Truncated spline regression was applied to capture nonlinear associations between predictors and HbA1c, and the comparison focused on linear versus quadratic specifications. The selection of the best model was based on the minimum GCV value. The model selection process indicated that the best specification was the linear truncated spline regression with two knot points. For FBG, the optimal knots were located at 159 mg/dL and 368 mg/dL, yielding the lowest GCV value of 3.5798. For LDL cholesterol, the best fit was achieved with knots at 183 mg/dL and 191 mg/dL, resulting in a GCV value of 4.3325. The predictive performance of this model was further supported by an R² value of 0.3861, indicating that the linear spline with two knots provides a better fit compared with the quadratic spline alternative. The spline approach showed a better fit based on GCV in depicting the changes in the influence of predictors on HbA1c, suggesting its potential as a more accurate predictive model for clinical and epidemiological purposes.

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