Jurnal Matematika, Statistika dan Komputasi
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Comparison of BDCL and Bootstrapping Bornhuetter Ferguson Methods in Claim Reserve Estimation (Case Study at Actuarial Consulting Firm X)
Full text linkRisk is an inherent uncertainty in human life. In the insurance industry, this requires companies to prepare claim reserves to cover potential future losses. Claim reserve estimation is generally carried out using a deterministic approach, but this method does not explicitly account for uncertainty. Therefore, this study applies development methods such as the semi-stochastic Bornhuetter-Double Chain Ladder (BDCL) method and the stochastic Bootstrapping Bornhuetter Ferguson method. The Bornhuetter Ferguson method is widely used due to its reliability, but the combination with bootstrapping techniques remains limited in the literature. Therefore, this study aims to compare the Bootstrapping Bornhuetter Ferguson method with the more commonly used BDCL method. The BDCL method allows separate calculation of IBNR and RBNS claim reserves, while Bootstrapping Bornhuetter Ferguson integrates bootstrapping techniques to improve reserve estimation accuracy. This study also adds reserve accuracy calculations using Mean Absolute Percentage Error (MAPE) and Mean Absolute Error (MAE). The data used consists of motor vehicle claim data with a quarterly observation period from 2017 to 2021. The results show that the MAPE value of the BDCL method is 12.62%, while the Bootstrapping Bornhuetter Ferguson method produces a MAPE of 8.10%. This indicates that the Bootstrapping Bornhuetter Ferguson method outperforms the BDCL method in calculating claim reserve estimate
Evaluation of NMF-VAE Integrative Approach for Biclustering and Glioblastoma Biomarker Identification
Full text linkGlioblastoma (GBM) represents the most aggressive primary brain tumor with poor prognosis. This research develops a novel computational framework that merges the strengths of Non-negative Matrix Factorization (NMF) with Variational Autoencoder (VAE) to improve biclustering performance in GBM gene expression data analysis. Using the GSE4290 dataset, this study analyzes gene expression data from 180 samples (136 tumors and 44 normal controls). The implementation of the NMF-VAE method successfully identified 10 biclusters with coherence values of 0.711 and variance of 0.713, validated through latent space visualization and reconstruction error analysis (15-50 MSE). Differential expression analysis identified three main potential biomarkers: ANXA2, TNFRSF1A, and NAMPT, which demonstrated significant expression changes (fold change 2.5, 2.0, and 3.0) and correlated with tumor cell proliferation, inflammation, and energy metabolism. Visualization of bicluster patterns and gene expression value distributions confirmed the consistency of these biomarkers overexpression in tumor samples. These findings provide new insights into the development of gene expression-based treatment strategies for GBM patient
Application of Autoregressive Integrated Moving Average (ARIMA) for Forecasting Inflation Rate in Indonesia
Full text linkInflation is one of the indicators to maintain economic stability. Controlling inflation reflects the success of economic growth, while very high or volatile inflation can lead to economic instability. The purpose of this research is to forecast the time series data of inflation rate in Indonesia until the end of 2024 using ARIMA method. The data used in this study are secondary data of monthly inflation rates in Indonesia from January 2003 to May 2024 obtained from the Bank Indonesia website. Based on the research results, the optimal model for forecasting the inflation rate in Indonesia until the end of 2024 is ARIMA (1,0,1) with a MAPE of 6.91%. The forecasting results show a stable and not too significant increase and are still within the target range set by Bank Indonesia and the Government, which is between 1,5% and 3,5% for 2024.
Inflasi merupakan salah satu indikator untuk menjaga kestabilan ekonomi. Pengendalian inflasi mencerminkan keberhasilan pertumbuhan ekonomi, sementara inflasi yang sangat tinggi atau fluktuatif dapat mengakibatkan ketidakstabilan ekonomi. Tujuan dari penelitian ini adalah untuk melakukan peramalan terhadap data deret waktu laju inflasi di Indonesia hingga akhir tahun 2024 dengan menggunakan metode ARIMA. Berdasarkan hasil penelitian, diperoleh model optimal untuk meramalkan laju inflasi di Indonesia hingga akhir tahun 2024 adalah ARIMA(1,0,1) dengan MAPE sebesar 6,91%. Hasil peramalan menunjukkan peningkatan stabil dan tidak terlalu signifikan serta masih berada dalam kisaran target yang ditetapkan oleh Bank Indonesia dan Pemerintah, yaitu antara 1,5% dan 3,5% untuk tahun 2024
Survival Analysis of Chronic Kidney Disease (CKD) Patients Undergoing Hemodialysis at RSUD Ratu Zalecha Martapura
Full text linkThe kidneys play an important role in excreting the body\u27s metabolic waste. The progressive decline in kidney function triggers Chronic Kidney Disease (CKD) which can be fatal if it’s not treated by undergoing regular hemodialysis or kidney transplantation. Research related to the effectiveness of the survival time of CKD patients is still limited, therefore this study aims to analyze the survival of CKD patients undergoing hemodialysis at Ratu Zalecha Martapura Hospital using survival analysis. The data collection method used purposive sampling. The research data were obtained from secondary source of medical records of 335 CKD patients who underwent hemodialysis during the observation in period from January 2022 until October 2024. The survival analysis methods used include Kaplan-Meier and Log-Rank tests for estimation of the survival function and Cox Proportional Hazard regression models by comparing 3 methods of handling co-occurrence (ties) namely Breslow, Efron, and Exact to identify factors that affect patient survival. The results showed that CKD patients without comorbidities had a higher survival chance than patients with hypertension, diabetes mellitus, and cardiovascular disease. In comparing the methods of handling ties, Exact method was the most appropriate for the data with the smallest Akaike Information Criterion (AIC) value of 481.3439. In addition, it was found that the factors that significantly influenced the length of CKD patient’s survival were hypertension status, diabetes mellitus status, and cardiovascular status
Binary Logistic Regression Analysis of Quarter-Life Crisis Symptoms on Sleep Difficulties in Early Indonesian Adulthood
Full text linkQuarter-life crisis and sleep difficulties are psychological phenomena commonly experienced during early adulthood. A 2017 LinkedIn survey revealed that 75% of respondents had experienced a quarter-life crisis. The WHO in 2020 reported that 19.1% of the global population suffered from sleep difficulties. In Indonesia, a similar trend has been observed. This study aims to identify quarter-life crisis symptoms that influence sleep difficulties among individuals in early adulthood, using a binary logistic regression model. Binary logistic regression is used when the response variable is dichotomous, estimating the probability of an outcome based on several predictor variables. This quantitative research uses secondary data from the fifth wave of the Indonesian Family Life Survey (IFLS 5). The response variable is sleep difficulty (yes/no), while the predictor variables include aspects of psychological health and coping efforts, such as difficulty concentrating, feeling disturbed, feeling pressured, requiring effort, inability to start something, hope for the future, future expectations, feeling of fear, feeling isolated, life satisfaction, happiness, religious obedience, and smoking behavior. The results showed that among females, significant predictors included difficulty concentrating, feeling disturbed, fear, isolation, and happiness. Among males, significant predictors included difficulty concentrating, feeling disturbed, requiring effort, inability to start something, fear, and smoking behavior. These results indicate that certain psychological symptoms related to quarter-life crisis significantly affect sleep difficulties, with different patterns between genders. It can be concluded that gender-specific psychological interventions may help reduce sleep-related issues among early adults experiencing a quarter-life crisis
Forecasting Nickel Prices in Indonesia Using ARIMA, SVR, and Hybrid ARIMA-SVR Approach
Full text linkNickel production plays a key role in reducing reliance on fossil fuels, supporting the 7th Sustainable Development Goals (SDGs) on clean and affordable energy. As the world\u27s largest nickel ore producer, Indonesia significantly influences global market dynamics. This study evaluates the accuracy of ARIMA, SVR, and hybrid ARIMA-SVR models in forecasting Indonesia’s daily nickel futures prices for 2023 using historical data from official website investing.com. The results indicate that SVR outperforms the other models, achieving the lowest MAPE of 0.2532% with the Radial Basis Function (RBF) kernel and optimized parameters , and selected through grid search method which gives the minimum RMSE and MAE values as well. Accurate nickel price forecasting is essential for investors, mining companies, and policymakers to optimize production planning, manage risks, and enhance market stability. However, this study relies solely on historical price data, without considering external factors such as geopolitical events and market shocks, highlighting the need for future research incorporating broader economic indicators and alternative modeling approache
Partition Dimension of the Sum Product of Complete Graph K_1 and Saw Graph GR_n
No full textLet and let denote the distance between dan . The distance of to a subset is denote by where Furthermore, suppose is an ordered partition with for then the representation of a vertex with respect to is the ordered k-tuple dinoted by . The partition is called a distinguishing partition of if for every . A distinguishing partition of with the smallest cardinality is called the minimum distinguishing partition of , and its cardinality is called the partition dimension of . The purpose of this study is to determine the partition dimension of the join graph and . By applying the concepts of equivalent vertices and vertices of the same level, it is shown that the partition dimension of the graph is where is a natural number
Determining Factors that Influence Unmet Need For Family Planning Using Geographically Weighted Logistic Regression With LASSO:
Full text linkBinary logistic regression is a regression used for categorical response variables with two possibilities: success or failure. This regression is a global model, making it inappropriate for spatial data. Binary logistic regression was then developed into geographically weighted logistic regression (GWLR). GWLR considers location factors into the model through a weight function. Nevertheless, GWLR is unable to overcome multicollinearity issue. Multicollinearity can cause the estimated parameters to be insignificant, thus it needs to be solved. A method to deal with multicollinearity is least absolute shrinkage and selection operator (LASSO). LASSO is applicable to various areas, including health, namely in the case of unmet need for family planning (FP). Unmet need for FP refers to productive-age women who do not wish to have more children or wish to postpone having children without using contraceptive methods. This study aims to obtain GWLR model with LASSO and influential factors, and acquire the performance of GWLR model with LASSO on unmet need for FP in South Sulawesi. The AIC value of the GWLR with LASSO model, which is 31,918, is less than the AIC value of the GWLR without LASSO, which is 38,879. This implies that GWLR with LASSO method is able to model unmet need for FP better than GWLR model. In addition, it was obtained that the status of unmet need for FP in 22 districts/cities was affected by the percentage of women with junior high school education or equivalent or lower, number of high-fertility women, percentage of husbands/families who refuse family planning, and number of KB staffs, while there were 2 districts/cities where the status of unmet need for KB was determined by the number of high-fertility women, percentage of husbands/families who refuse family planning, and number of FP staffs
On Convergence in Norm of Functions in L^p Spaces by Convolution Using Dilation Kernel
Full text linkIn this paper, we investigate the convergence in norm of functions in L^p (R^d) by convolution. We use dilation kernel from L^1 as approximation identity and prove convergence of a function using convolution with dilation kernel in norm ‖∙‖_p for 1≤p<∞ and norm ‖∙‖_∞ for p=∞
Fibonacci Prime Labelling on the Class of Flower Graphs
Full text linkGraph labeling is one of the significant topics in graph theory. One of its interesting variants is Fibonacci prime labeling, a special type of labeling that assigns Fibonacci numbers as vertex labels while satisfying certain conditions. A graph labeling is an assignment of labels (elements of some set) to elements of a graph, usually the vertices or the edges (or both) of the graph. Several previous studies have shown that some classes of graphs, such as cycle graphs, fan graphs, and umbrella graphs, satisfy the criteria for Fibonacci prime labeling. Moreover, previous research has proven that flower graphs and double flower graphs admit prime labeling. Motivated by these findings, this study aims to explore whether these two classes of graphs also admit Fibonacci prime labeling. This exploration seeks to identify a potential relationship between prime labeling and Fibonacci prime labeling in these graph classes. This research focuses on graphs with an even number of vertices. The methods used include literature review and mathematical proof. The novelty of this study lies in extending the results of prime labeling to Fibonacci prime labeling for flower and double flower graphs. The results show that both graph classes with an even number of vertices belong to the class of graphs that admit Fibonacci prime labeling