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Jl. Prof. Dr. Ing. B. J. Habibie, Moutong, Tilongkabila, Kabupaten Bone Bolango, Gorontalo, Indonesia
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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 191 Documents
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Optimal IDX30 Stock Portfolio Construction Using a Two-Constraint Mean-Variance Model with Robust S-Estimation Anis Faiqo Tuzzainiyah; Evy Sulistianingsih; Nurfitri Imro’ah
Jambura Journal of Mathematics Vol 8, 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.v8i2.39603

Abstract

The capital market plays an important role in the economy by providing investment instruments for investors and financing sources for companies. A capital market portfolio consists of a collection of financial assets, such as stocks, constructed to achieve an optimal return while reducing investment risk. Mean-variance portfolio construction is highly sensitive to parameter estimation errors. Therefore, a robust estimation approach is employed to obtain more stable parameter estimates by minimizing the influence of outliers. This study aims to construct an optimal stock portfolio through diversification, determine stock weights using a two-constraint mean-variance model with robust S-estimation, calculate the expected return and risk, and evaluate portfolio performance. The analysis was conducted using the closing prices of stocks included in the IDX30 Index from October 2024 to September 2025. The results identified nine stocks with positive expected returns from five different sectors. Based on the stock selection criteria, two optimal portfolios were constructed. Portfolio 1 consists of ASII, BRPT, INDF, PGAS, and TLKM, whereas Portfolio 2 consists of ASII, ANTM, INDF, PGAS, and TLKM. Portfolio 1 generates an expected return of 0.137% with a risk of 2.226%, while Portfolio 2 generates an expected return of 0.097% with a risk of 1.319%. Based on the Sharpe and Treynor ratios, Portfolio 1 demonstrates relatively better performance than Portfolio 2.
Geographically and Temporally Weighted Log-Logistic 3-Parameter Regression Model for Poverty Severity Index : A Case Study on East Java Province Nur Huda; Purhadi Purhadi; Tintrim Dwi Ary Widhianingsih
Jambura Journal of Mathematics Vol 8, 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.v8i2.38021

Abstract

This study proposes the Geographically and Temporally Weighted Log Logistic 3 Parameter Regression (GTWLL3R) model as a novel extension of LL3R that simultaneously captures spatial and temporal heterogeneity in poverty severity index. Using the poverty severity index of East Java Province for 2022–2024, local parameters were estimated through an fixed Gaussian kernel weighting matrix based on spatial and temporal distances, with optimization using the Newton–Raphson algorithm. Model performance was evaluated using the corrected Akaike Information Criterion (AICc). The results show that GTWLL3R outperformed the LL3R and GWLL3R models, achieving the lowest AICc value of 18.311, which indicates substantially better model fit and stronger explanatory capability. The estimated coefficients vary across districts/cities and time periods, revealing different patterns of predictor effects on poverty severity index. Based on significant predictor variables, the districts/cities were classified into three clusters. These findings demonstrate that integrating LL3R into the GTWLL3R framework provides a more flexible and accurate approach for analyzing spatiotemporal poverty dynamics and offers stronger evidence for targeted poverty alleviation policies.
Hyperparameter-Optimized Gradient Boosting for Daily Rainfall Prediction Using BMKG Meteorological Data in Malang Regency, Indonesia Mohamad Arif Abdul Syukur; Suhartono Suhartono; Mochamad Imamudin
Jambura Journal of Mathematics Vol 8, 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.v8i2.38554

Abstract

Weather conditions significantly affect many aspects of modern life, including transportation, tourism, agriculture, and disaster risk management, particularly in relation to rainfall. Consequently, reliable meteorological information is essential for supporting daily decision-making, making rainfall prediction increasingly important. This study develops a daily rainfall prediction model using gradient boosting based on daily meteorological data obtained from the Indonesian Agency for Meteorology, Climatology, and Geophysics (BMKG). The dataset includes date, minimum, maximum, and average temperatures, relative humidity, sunshine duration, maximum and average wind speeds, and wind direction, with daily rainfall as the target variable. Four chronological train-test split scenarios were evaluated. The first scenario produced an RMSE of 13.97, an MAE of 7.96, and an R^2 value of 0.14. The second scenario yielded an RMSE of 12.81, an MAE of 8.72, and an R^2 value of 0.17. The third scenario achieved an RMSE of 12.21, an MAE of 7.70, and an R^2 value of 0.20, whereas the fourth scenario obtained an RMSE of 10.31, an MAE of 7.11, and an R^2 value of -0.27. Considering both prediction error and generalization capability, the third scenario was selected as the best-performing model. The main contribution of this study lies in demonstrating the effectiveness of hyperparameter optimization in improving the stability of rainfall prediction under complex tropical climatic conditions. Practically, the proposed model may support BMKG and regional policymakers in Malang Regency in hydrometeorological disaster mitigation and agricultural planning.
Modeling and Optimizing State-Based Electricity Consumption Distributions in Dodoma Region, Tanzania Using Hidden Markov Models Eliasi M Jeremiah; Ramkumar T Balan; Jairos K. Shinzeh
Jambura Journal of Mathematics Vol 8, 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.v8i2.34047

Abstract

The aim of this study is to model and optimize state-based Electricity Consumption Distributions in Dodoma Region, Tanzania using Hidden Markov Models. The research is specifically aimed at the identification of hidden consumption states, and the determination of the best number of hidden states to enhance the state distributions identification. A quantitative approach was utilized based on monthly TANESCO electricity demand time series data for the years 2010-2025. The estimation involved the calculation of state transition probabilities, model diagnostics testing, and evaluation of forecasting performance based on different hidden state configurations. Model selection was based on extensively documented statistical criteria, namely the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). Empirical results revealed that a three-state HMM achieved the best performance with the lowest AIC (5492.480) and BIC (5707.104) values relative to models of two to ten states. The diagnostic tests concluded that segmenting the series into latent states improved statistical attributes such as normality, homoscedasticity, and stationarity that otherwise failed in the original unsegmented data. For instance, State 1 residuals were homoscedastic (Breusch-Pagan p = 0.22), and State 3 demonstrated stationarity (ADF p ≈ 0.01), enhancing interpretability and model fit. These findings show that three states bring optimal fit for prediction, and each state fulfils the assumption of homoscedasticity, as all states follow a normal distribution. The study recommends that energy policymakers and utility providers integrate HMM-based forecasting approaches to improve decision-making in regions with dynamic and complex electricity usage patterns.
Optimal Control of an Age-Structured Pneumonia Transmission Model with Vaccination and Treatment Strategies Dwi Lestari; Nikenasih Binatari; Eminugroho Ratna Sari
Jambura Journal of Mathematics Vol 8, 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.v8i2.38190

Abstract

This research aims to apply optimal control to model the pneumonia disease using a system of ordinary differential equations. We developed based on the SIR pneumonia epidemic model. We divided the population into two groups: children and the elderly. The optimal controls illustrate the effectiveness of vaccination and treatment in preventing new infections among both children and the elderly. The Pontryagin’s maximum principle is used to define the optimal controls, and the resulting optimality system is formulated and solved numerically. Numerical simulations have been performed. It was found that combining vaccination and treatment effectively reduces the number of pneumonia infections. In fact, when we change the cost scenario, we see changes in the control variables. This study supports the joint implementation of vaccination and therapeutic interventions to control pneumonia transmission among children and the elderly, particularly in developing countries where economic limitations, inadequate infrastructure, and distribution barriers restrict vaccine access.
The Expected-Based Method of Value-at-Risk Prediction Jacob Stevy Seleky; Lina Cahyadi Cahyadi; Sausan Ramadhani
Jambura Journal of Mathematics Vol 8, 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.v8i2.37273

Abstract

Value-at-Risk (VaR) remains a fundamental risk measure in financial risk management, providing an indicator for managing capital allocation and avoiding worst-case risk scenarios. Traditionally its defined as a quantile of the loss distribution. However, its computation depends critically on the existence and tractability of the inverse cumulative distribution function (CDF), which may not be available in closed form for complex or empirical distributions. This paper proposes an expectation-based simulation framework for VaR estimation that avoids explicit inversion of the CDF. The method approximates VaR by taking the expectation of order statistics from repeated sampling, effectively constructing a variance-reduced Monte Carlo estimator of the quantile. We provide a rigorous theoretical foundation for the proposed approach, including strong consistency, asymptotic normality, and a bias–variance decomposition. In particular, we show that the estimator achieves variance reduction proportional to the number of simulations while remaining consistent with the classical definition of VaR. Furthermore, under heavy-tailed distributions, the method demonstrates enhanced stability compared to traditional historical simulation, which is known to exhibit high tail variability. Extensive simulation studies confirm the theoretical findings, showing significant improvements in mean squared error and backtesting performance. Overall, the proposed framework provides a flexible alternative for VaR estimation in settings where conventional inversion-based methods are infeasible or unreliable.
A Construction of a Smooth Travel Groupoid on a Spanning Tree Associated with Lotus Graphs Husnul Khotimah; Andi Tenri Ajeng Nur; Putri Nilam Cayo
Jambura Journal of Mathematics Vol 8, 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.v8i2.38029

Abstract

A travel groupoid is a binary system associated with a graph through an operation on its vertex set, while a smooth travel groupoid satisfies an additional smoothness condition. In this paper, we construct a smooth travel groupoid on a particular spanning tree associated with the lotus graph L(n). The spanning tree is obtained by deleting the edges u_i v_{i+1}, for 1 \leq i \leq n-1, from the lotus graph. Using the unique path between two vertices in this tree, we define a binary operation by assigning to each ordered pair the first step from one vertex toward the other. We prove that the resulting binary system satisfies the axioms of a travel groupoid and fulfills the smoothness condition. Explicit examples for L(2) and L(3) are also presented to illustrate the construction.
On Deformed-Metric Equivalence of Hilbert Space Operators Amenya Collins; Victor Wanjala; John Matuya
Jambura Journal of Mathematics Vol 8, 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.v8i2.36685

Abstract

This paper introduces and studies a novel class of equivalence relations in operator theory, called deformed-metrically equivalent operators. Two operators S and T in B(H) are said to be deformed-metrically equivalent if there exists a positive operator P such that SPS = TT. This definition generalizes traditional metric equivalence by incorporating a positive deformation operator P, enabling a richer algebraic and spectral analysis. We establish several fundamental results, including the preservation of key operator classes such as normality, posinormality, and compactness under suitable commutativity conditions. Spectral inclusion relations are derived under invertibility assumptions, and the equivalence is shown to be stable under limits, tensor products, and functional calculus. Moreover, the set of all operators deformed-metrically equivalent to a given operator forms an affine space that is closed in the weak operator topology. These findings deepen the theoretical framework of operator equivalence and reveal new connections with well-studied classes such as posinormal, supraposinormal, and k-quasi n-power posinormal operators.
Parameter Estimation of a Climate-Based Dengue Mathematical Model in Bandung City Using the Particle Swarm Optimization Algorithm Sindi Meli Nur Afni; Khusnul Novianingsih; Ririn Sispiyati
Jambura Journal of Mathematics Vol 8, 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.v8i2.39153

Abstract

Dengue Hemorrhagic Fever (DHF) is spread through the bite of the Aedes aegypti mosquito and is affected by the environment, especially temperature and rainfall. The purpose of this study is to create a SEIR (Susceptible–Exposed–Infected–Recovered) mathematical model taking into account the effects of climate factors and to estimate the parameters of this model using the Particle Swarm Optimization (PSO) algorithm. The analyzed data consisted of monthly reports of the number of dengue fever cases, temperature, and rainfall for the city of Bandung in 2022–2023 and were smoothed using a moving average. The parameter estimation process was performed by minimizing the Mean Absolute Percentage Error (MAPE), and the numerical simulation of the model was performed using the fourth-order Runge–Kutta method (RK4). The results of this study show that the model has two equilibrium points: a disease-free equilibrium point and an endemic equilibrium point, and the stability of the equilibrium points depends on the basic reproduction number R0. The best parameters obtained were β0 = 3.5553, β1 = 0.0021, β2 = 0.0001, σ = 7.5, µ = 0.0011, and γ = 3.6865, with an MAPE value of 0.1740 or 17.40%. These findings indicate that the model is able to represent the pattern of dengue fever spread with a low level of prediction error. Sensitivity analysis showed that the recovery rate parameter (γ) was the most responsive to changes in the model.
Joint Life Long-Term Care Insurance: A Semi-Markov Multi-State Model Integrating LTC Prevalence and Mortality Trends Roro Anteng; Adhitya Ronnie Effendie
Jambura Journal of Mathematics Vol 8, 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.v8i2.39021

Abstract

This study develops a two-person joint-life long-term care (LTC) insurance pricing framework for married couples by incorporating mortality and LTC risks within a semi-Markov-inspired multi-state model. The transition intensity structure accounts for Gompertz mortality, potential common-shock events, and a duration-dependent bereavement effect. LTC-related transition intensities are adjusted using proportional factors, while the transition probabilities are approximated using a matrix-exponential procedure and applied to the calculation of net single premiums.A numerical case study is presented for a married couple aged 62 and 60 under a 20-year coverage period. The alternative benefit designs include mortality protection, LTC annuity protection, and a combined design integrating death and LTC benefits. The results indicate mortality dependence between spouses through the common-shock and post-bereavement mechanisms and show that broader benefit coverage produces a higher net single premium.The main contribution of this study is an actuarial pricing framework for two associated individuals that jointly incorporates spousal mortality dependence, LTC incidence, and combined death and LTC benefits in a unified multi-state structure.

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