Jurnal Matematika, Statistika dan Komputasi
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Analysis of Open Unemployment Rates in Indonesia Based on GRDP and the Percentage of Poor Population Using Nonparametric B-Spline Regression
Get PDFOpen Unemployment Rate (OUR) is a crucial indicator of the condition of the job market and the economy in Indonesia. This research is to modeling and analyzes the impact of GRDP and the percentage of poor population to the OUR in Indonesia using nonparametric B-Spline regression. The study applied B-Spline model due to the model’s property of handling non-linear associations without imposing any distributional assumptions. The research a used secondary data sourced from BPS Indonesia in 2024, which included 38 provinces in Indonesia. The analysis outcomes show that optimal model is achieved when the order was set at 2 for both GRDP and the percentage of poor population with one knot set at GRDP (1.055) and two knots set at the percentage of poor population (6.813333 and 11.583333) which gave a minimum GCV produced at 1.577369. The model’s coefficient of determination value of 0.7454 indicates that the model can explain 74.54% of the variation in the OUR is explained by GRDP and the percentage of poor population, with the remaining 25.46% is impacted by factors beyond the model
Dynamic Analysis of the SIRS Model with a Type III Holling Function on the Corrosion Distribution of Bridge Reinforcement Steel in Coastal Areas
Get PDFThis study discusses the dynamics of corrosion spread on reinforced concrete bridge reinforcement in coastal areas using the SIRS mathematical model approach and considering the Holling type III function. The model built, can be seen how corrosion appears, spreads, and persists based on the influence of interaction parameters between healthy reinforcement and reinforcement that has experienced damage. In addition, this model can be analyzed dynamically including the equilibrium point, local stability and basic reproduction number. The simulation results show that when the basic reproduction number , corrosion cannot persist and the system will return to a corrosion-free condition. However, when , corrosion is able to spread and persist so that some of the reinforcing steel remains in a corroded condition. Parameter analysis shows that increasing the ratio of the corrosion propagation rate to the recovery rate significantly increases the likelihood of corrosion development and long-term persistence. This ratio represents the intensity of interaction between the reinforcement in good condition and the corroded reinforcemen
Connectivity Indices of Coprime Graphs over Generalized Quaternion Groups of a Certain Order
Get PDFThe generalized quaternion group is a non-abelian group of order that exhibits certain structural similarities with the dihedral group. It is generated by two elements that satisfy specific defining relations. Meanwhile, a coprime graph is constructed by representing the elements of a group as vertices, where two vertices are adjacent if the orders of the corresponding elements are coprime. In this study, we investigate coprime graphs derived from generalized quaternion groups, particularly when the group order is given by , with being a prime number. Based on the structural properties of these graphs, we compute several connectivity indices, including the First and Second Zagreb indices, the Wiener index, the hyper-Wiener index, the Harary index, and the Szeged index
Prime Labeling of Special Graph Classes Constructed from Dutch Windmill Graphs
Get PDFLet G be a simple graph of order n. Prime labeling is a bijective function f:V(G)→{1,2,…,n} such that gcd(f(u),f(v))=1 for every pair of adjacent vertices u,v in G. A graph G that satisfies the definition of prime labeling is called a prime graph. The Dutch windmill graph D_r^n is a graph obtained by taking n copies of cycle graph C_r with a vertex in common. The double quadrilateral graph DQ is a graph constructed from two copies of C_4 and identifying one edge from each of them. The graph obtained by taking n copies of DQ and identifying one vertex of degree 3 from each of them as a common central vertex is called the double quadrilateral Dutch windmill graph DQ_n, for n≥1. Furthermore, graphs D_r^n and DQ_n becomes the base graph to construct two new graph classes, namely graph P_2 [D_r^n] and flower double quadrilateral graph FDQ_n. Both graph classes, constructed from the Dutch windmill graph, also contain even cycles. From previous research, it is known that graphs P_2 [D_4^n] and flower double quadrilateral graph FDQ_n have odd harmonious labeling. However, the determination of prime labeling on both classes is still an open problem. In this paper, we show that two classes of graphs constructed from Dutch windmill graphs with even cycles, namely graphs P_2 [D_4^n] and flower double quadrilateral graphs FDQ_n for n≥1 have a prime labeling. The result of this research shows that these graphs are prime graphs
Inflation Forecasting for Riau Province: A Comparison of Parametric ARIMA with Nonparametric Nadaraya-Watson Kernel Regression and B-Spline Methods
Get PDFForecasting inflation is crucial for assisting in the creation of sound economic strategies, particularly in key regions like Riau Province, one of the country\u27s hubs for the production of crude oil and palm oil. The economic peculiarities of Riau, which set it apart from other regions, lead to inflation patterns in this province that tend to deviate from the national average. Forecasting techniques are crucial for decision-making that promotes stability and overall regional economic planning. The parametric ARIMA method and the nonparametric Nadaraya-Watson Kernel Regression and B-Spline are used in this study to forecast inflation in Riau Province in 2025. While ARIMA is based on certain model assumptions, nonparametric methods are more flexible and can capture more complex patterns. The forecasting results using RMSE, ME, MAE, and MASE showed that the Nadaraya-Watson method performed the best out of the three methods tested. The forecasting results with Nadaraya-Watson Kernel Regression showed a stable decline in inflation, from 0.0464% in March to 0.0191% in August 2025
MODEL SPATIAL AUTOREGRESSIVE MOVING AVERAGE DENGAN PEMBOBOT ROOK CONTIGUITY: (Studi Kasus: Indeks Pembangunan Manusia Kabupaten/Kota di Pulau Kalimantan)
No full textThe Spatial Autoregressive Moving Average (SARMA) model is a regression model developed from the classical regression model. The classical regression model produces inaccurate conclusions when used to model spatial data because the assumption of independent errors is not met. The SARMA model has advantages in modeling spatial data that has a spatial effect on the lag of the dependent variable and error. This study aims to obtain a SARMA model and factors that significantly influence the Human Development Index (HDI) of districts and cities in Kalimantan in 2022 based on the SARMA model. The spatial weighting used in SARMA modeling is rook contiguity. The results of the study show that the SARMA model can model the HDI of districts and cities in Kalimantan. The factors that significantly influence the HDI of districts and cities in Kalimantan are the poverty rate, the open unemployment rate, and the number of hospital facilities.Regresi spasial merupakan pengembangan dari model regresi linier dengan mempertimbangkan pengaruh faktor lokasi. Model regresi spasial yang digunakan adalah Spatial Autoregressive Moving Average (SARMA). Penelitian ini bertujuan mendapatkan model SARMA dan faktor-faktor yang berpengaruh signifikan terhadap Indeks Pembangunan Manusia (IPM) kabupaten/kota di Pulau Kalimantan Tahun 2022 berdasarkan model SARMA. Hasil penelitian menunjukkan bahwa terdapat autokorelasi spasial pada data IPM kabupaten /kota di Pulau Kalimantan yang diperoleh dari uji Indeks Moran’s. Berdasarkan Uji lagrange multiplier, data IPM kabupaten/kota di Pulau Kalimantan dapat dimodelkan dengan model SARMA. Faktor-faktor yang berpengaruh signifikan terhadap IPM kabupaten/kota di Pulau Kalimantan berdasarkan model SARMA adalah persentase penduduk miskin, tingkat pengangguran terbuka, dan jumlah fasilitas rumah sakit
Pendekatan Minimum Variance Quadratic Unbiased Estimation dalam Analisis Regresi Data Panel dengan Pendugaan Komponen Galat Dua Arah Menggunakan Metode Biggers
Get PDFPanel data that have missing observations can be known as incomplete panel data. The model used is a two-way error component. The missing data estimation used is the Biggers method. This study aims to model the incomplete panel data regression of two-way error components on Manufacturing Company Stock Return data. The method used for estimating the error variance component is Minimum Variance Quadratic Unbiased Estimation (MIVQUE) with parameter estimation using Maximum Likelihood (ML). The method was applied to IDX data for 10 companies from 2014-2021. The results obtained using the MIVQUE method are σ ̂_v^2= 0.1142, σ ̂_μ^2=-0.0107, and σ ̂_λ^2=0.0068, for the ML method produces β ̂_0=0.0304719 〖 β ̂〗_1= -0.021107, and β ̂_2=0.0087936. Based on these methods, if there is an increase in the Debt to Equity Ratio, there is a decrease in the value of stock returns, and vice versa for Net Profit Margin
Optimization of Stock Portfolio Investment based on K-Means Clustering using Markowitz Method (A case study: IDX-MES BUMN17 Index)
Get PDFA stock portfolio is a combination of two or more equity securities invested over a specific period and under certain conditions. This research analyzes stock combinations that can be formed into an optimal portfolio using the Markowitz method. The Markowitz method is employed to maximize returns and minimize the risk of a portfolio. The data used in this study consists of daily closing prices from the IDX-MES BUMN17 index, one of the indices in Indonesian Stock Exchange, between January 2023 and December 2023. Based on the results obtained, two recommended portfolios are identified, known as the Minimum Variance Portfolio (MVP) and Tangency Portfolio. The optimal portfolio can serve as an option depending on the investor\u27s risk profile
Computing The First Zagreb Index, The Wiener Index and The Gutman Index of The Power of Dihedral Group Using Python
Get PDFThis paper presents a computational study on three classical topological indices—the First Zagreb Index, Wiener Index, and Gutman Index—within the context of power graphs of the dihedral group , where is a positive integer representing half the order of the group. These indices are fundamental in mathematical chemistry and graph theory, serving as quantitative descriptors of graph structure and connectivity. The methodology involves constructing power graphs derived from and calculating the indices using Python programming, supported by the NetworkX, Matplotlib, and Gradio libraries. Numerical simulations were conducted for varying values of , revealing consistent algebraic patterns and insights into the structural complexity of the corresponding graphs. Additionally, an interactive Python-based interface is developed to facilitate real-time computation and visualization, thus promoting further exploration and application in algebraic graph theory
Fuzzy Time Series Saxena Easo on Forecasting the Number of Dengue Hemorrhagic Fever Cases in Bengkulu Province
Get PDFDengue Hemorrhagic Fever (DHF) is a viral infectious disease that is transmitted through mosquitoes and is a public health problem in the world. Untreated Dengue Hemorrhagic Fever (DHF) can trigger extraordinary events (KLB), severe dengue and even cause death. Tropical countries like Indonesia cause cases of Dengue Hemorrhagic Fever (DHF) to be found in almost all provinces. This disease is endemic, especially in Bengkulu Province. The increase and decrease in the number of cases can also be seen using forecasting methods. The time series forecasting method used in this research is the Saxena-Easo fuzzy time series. Where this method is a modification and refinement of the previous method, namely the Stevenson & Porter fuzzy time series method. The Stevenson & Porter method changes the actual data into percentage change which was then developed by Saxena Easo with modifications to the number of data intervals. The data developed by Saxena Easo is dividing the number of intervals into sub-intervals based on the number of frequencies. This research aims to predict the number of Dengue Hemorrhagic Fever cases in Bengkulu Province from the 1st week of 2022 to the 24th week of 2024, and compare it with existing data on the number of cases. Based on the research, the results of the accuracy level of the Mean Absolute Percentage Error (MAPE) in forecasting the number of cases of Dengue Hemorrhagic Fever in Bengkulu Province using the FTS Saxena Easo method obtained a value of 0.359637893 or 3.5%, so the forecast accuracy value obtained is included in the criteria for very good forecasting, because it has an accuracy value below 10%. It can be said that the comparison between actual data and forecasts is not much different