Jurnal Matematika, Statistika dan Komputasi
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No full textThe Sylvester-Kac matrix is also known as the Clement matrix The Sylvester-Kac matrix is widely used and applied both in processing, graphs and other fields. The Sylvester-Kac matrix developed in the paper is the T-Sequence-Sylvester-Kac matrix The calculation of the determinant, and inverse has always been a challenge for mathematicians to find. In this paper will be given the formulation of determinant, and inverse of the T-Sequence-Sylvester-Kac matrixMatriks Sylvester-Kac disebut sebagai matriks clement. Matriks Sylvester-kac banyak digunakan dan diaplikasikanbaik di bidang komputasi, graf maupun lainnya. Matriks Sylvester-Kac yang dikembangkan dalam penelitian iniadalah matriks T-Sequence-Sylvester-Kac. Perhitungan determinan, dan inverse selalu menjadi tantanganmatematikawan untuk menemukannya. Dalam penelitian ini akan diberikan rumusan determinant dan invers darimatriks T-Sequence-Sylvester-Ka
Implementation Vector Autoregressive (Var) On Rice Production and Rice Productivity Data in Indonesia
Get PDFVector Autoregressive (VAR) is a statistical model used to analyze multivariate time series, especially in time series where the variables have a relationship that influences each other over time. This study aims to determine the relationship between rice production and rice productivity in Indonesian. The data used in this study is secondary rice commodity data based on rice production and rice productivity in Indonesian from January 2014 to December 2018. The Augmented Dickey-Fuller method in this study was used to carry out a stationary test on the data. The ACF and PACF graphs show that rice commodity data based on rice production and rice productivity can be modeled using VAR. Based on the VAR(1) model, that rice production and rice productivity influence each other. The R2 and Adjusted R2 values for each partial equation of the VAR model (1) tend to be small so that the diversity of the models for each equation cannot be explained by the variables of rice production and rice productivity in Indonesian.Vector Autoregressive (VAR) adalah suatu model statistik yang digunakan untuk menganalisis deret waktu multivariat, terutama pada deret waktu yang variabel-variabelnya memiliki hubungan yang saling mempengaruhi terhadap waktu. Penelitian ini bertujuan untuk mengetahui hubungan produksi padi dan produktivitas padi di Indonesia. Data yang digunakan pada penelitian ini adalah data sekunder komoditas beras berdasarkan produksi padi dan produktivitas padi di Indonesia dari bulan Januari 2014 sampai dengan Desember 2018. Metode Augmented Dickey-Fuller pada penelitian ini digunakan untuk melakukan uji stasioner pada data. Grafik ACF dan PACF menunjukkan bahwa data komoditas beras berdasarkan produksi padi dan produktivias padi dapat dimodelkan dengan menggunakan VAR. Berdasarkan model VAR(1), bahwa produksi padi dan produktivitas padi saling mempengaruhi satu sama lain. Nilai R2 dan Adjusted R2 tiap persamaan parsial model VAR (1) cenderung kecil sehingga keragaman model masing-masing persamaan belum dapat dijelaskan oleh variable produksi padi dan produktivias padi di Indonesia
Modeling the Hotel Tax Revenue in Central Lombok using Nonparametric Regression
Get PDFIn Central Lombok Regency, the hotel tax is one of the highest incomes contributing to Regional Original Revenue. A hotel tax is a tax on services provided by the hotel. This research aims to estimate the nonparametric kernel regression curve on hotel tax revenue data in Central Lombok. The method used is nonparametric kernel regression analysis with the seven kernel functions. The results of the analysis with the Generalized Cross Validation (GCV) criteria, the optimal bandwidth values generated by the seven kernel functions have varying values. Although the bandwidth values vary, the resulting estimation results are similar, and the comparison of the Mean Square Error (MSE) values of the seven kernel functions is not significantly different
Kestabilan Lokal Titik Ekuilibrium Model Transmisi Penyakit Tuberkulosis
Get PDFA crucial part of illness prevention over the past few decades has been played by mathematical models. The dynamic system can be used to characterize the TB infection process. For the purpose of developing future prevention strategies, it is crucial to comprehend the effect of vaccination approach on the control of TB. We investigated the impact of vaccination strategies on TB disease transmission through a dynamic model. The model discussed involves logistical population growth. The purpose of this discussion is to analyze the local stability of the equilibrium point of the TB disease transmission model. Numerical simulations are provided to illustrate the theoretical results. The existence and local stability of the model equilibrium point depends on the basic reproduction number analytically. Based on secondary data, the basic reproduction number values are 0.98 and 4.12, respectively. Numerical simulations for these two values support the analysis results obtained. If the basic reproduction number is less than one, then the transmission of TB disease can be eradicated. However, if the basic reproduction number is more than one, the vaccination strategy is not sufficient to control TB transmission.Model matematika beberapa dekade terakhir memainkan peran penting dalam pengendalian suatu penyakit. Dinamika sistem dapat menggambarkan proses penularan penyakit tuberkulosis (TB). Pengaruh strategi vaksinasi terhadap penularan penyakit TB penting untuk dipahami dalam rangka pengembangan strategi pencegahan di masa depan. Kami menyelidiki dampak strategi vaksinasi pada penularan penyakit TB melalui model dinamis. Model yang dibahas melibatkan pertumbuhan penduduk secara logistik. Tujuan pembahasan ini adalah menganalisis kestabilan lokal titik ekuilibrium model penularan penyakit TB. Simulasi numerik diberikan untuk mengilustrasikan hasil teoritis. Eksistensi dan kestabilan lokal titik ekuilibrium model bergantung pada bilangan reproduksi dasar secara analitik. Berdasarkan data sekunder diperoleh nilai bilangan reproduksi dasar masing-masing sebesar 0,98 dan 4,12. Simulasi numerik untuk dua nilai tersebut mendukung hasil analisis yang diperoleh. Jika bilangan reproduksi dasar kurang dari satu maka penularan penyakit TB dapat diberantas akan tetapi, sebaliknya jika bilangan reproduksi dasar lebih dari satu maka strategi vaksinasi yang dilakukan belum cukup untuk mengendalikan penularan penyakit TB
Ukuran-Ukuran Aktuaria untuk Data Besar Klaim Berdistribusi Inverse Gaussian
Get PDFAn insurance company must be able to manage risks in the form of claims submitted by policyholders. There are several risk measures or actuarial measures that can be used to predict future risks and help companies prepare reserves. These actuarial measures are Value at Risk (VaR), Tail Value at Risk (TVaR), Tail Variance (TV), and Tail Variance Premium (TVP). In this article, we will discuss these actuarial measures for inverse Gaussian distributed claim severity. The Kolmogorov-Smirnov test is used to test the fit of the inverse Gaussian distribution. The maximum likelihood estimator is used as a method to estimate the parameters of the inverse Gaussian distribution. The data used in this article is data on partial loss claims for motor vehicle insurance insurance company PT. ABC in 2019 Category 1 in all regions. However, after testing the goodness of fit of the distribution using the Kolmogorov-Smirnov test for region 3, it did not come from a population with an inverse Gaussian distribution. So the data used to proceed to the actuarial measures estimation stage is only region 1 and region 2. Based on the results of calculating the actuarial measures for inverse Gaussian distributed claim severity, it can be concluded that the value of losses expected by a company can be calculated by taking into account the actuarial measures for claim severity on motor vehicle insurance in Indonesia.Suatu perusahaan asuransi harus mampu mengelola risiko berupa klaim yang diajukan pemegang polis. Ada beberapa ukuran risiko atau ukuran aktuaria yang dapat digunakan untuk memprediksi risiko di masa yang akan datang dan membantu perusahaan mempersiapkan cadangan. Ukuran-ukuran aktuaria tersebut adalah Value at Risk (VaR), Tail Value at Risk (TVaR), Tail Variance (TV), dan Tail Variance Premium (TVP). Dalam artikel ini akan dibahas ukuran-ukuran aktuaria tersebut untuk data besar klaim berdistribusi inverse Gaussian. Uji Kolmogorov-Smirnov digunakan untuk menguji kecocokan distribusi inverse Gaussian. Penaksir kemungkinan maksimum digunakan sebagai metode untuk menaksir parameter distribusi inverse Gaussian. Data yang digunakan dalam artikel ini adalah data besar klaim partial loss asuransi kendaraan bermotor perusahaan asuransi PT. ABC tahun 2019 Kategori 1 pada semua wilayah. Namun, setelah dilakukan uji kecocokan distribusi menggunakan uji Kolmogorov-Smirnov untuk wilayah 3 tidak berasal dari populasi yang berdistribusi inverse Gaussian. Sehingga data yang digunakan untuk melanjutkan ke tahap penaksiran ukuran aktuaria hanya wilayah 1 dan wilayah 2. Berdasarkan hasil dari perhitungan ukuran risiko atau ukuran aktuaria pada data besar klaim berdistribusi inverse Gaussian, dapat disimpulkan bahwa nilai kerugian yang diharapkan oleh suatu perusahaan dapat dilakukan dengan memperhitungkan ukuran-ukuran aktuaria untuk data besar klaim asuransi kendaraan bermotor di Indonesia
Comparative Analysis of Ridge, LASSO, and Elastic Net Regularization Approaches in Handling Multicollinearity for Infant Mortality Data in South Sulawesi
Get PDFInfant mortality rate is a crucial indicator for assessing the health and infant care quality in a region. In the effort to reduce infant mortality rates, regression analysis serves as a tool to identify influential factors. However, regression analysis often encounters the challenge of multicollinearity, which involves high correlation among predictor variables. To address this issue, various regularization techniques can be applied, such as ridge regression, least absolute shrinkage and selection operator (LASSO), and elastic net. Ridge regression aims to control coefficient variance, while LASSO directs some coefficients to zero, functioning as variable selection. Elastic net combines the strengths of both methods by merging ridge and LASSO regularization. The objective of this research is to evaluate the performance of ridge regression, elastic net, and LASSO methods in handling multicollinearity issues, utilizing infant mortality rate data in South Sulawesi Province. The results indicate that the elastic net method outperforms both Ridge and LASSO methods. The best-performing model is obtained through elastic net with a coefficient of determination value of 60.81%, whereas ridge and LASSO methods yield coefficient of determination values of 54.11% and 58.18%, respectively. This demonstrates that the application of the elastic net method is capable of producing more accurate results in modeling the variables within the analysis of infant mortality rate data compared to other methods
Analisis Klasifikasi K-Means Terhadap Pemahaman Konsep dan Self-Efficacy: Menjelajahi Hubungan dalam Konteks Pendidikan
No full textConcept understanding and self-efficacy are two important aspects of mathematics learning that are interrelated. However, there is still debate about the relationship between these two aspects in the context of mathematics learning. Therefore, this study was conducted to analyze the classification of concept understanding and self-efficacy using K-means clustering with a sample of grade VIII students from three selected schools in Wolowaru District and Kelimutu District, Ende Regency, NTT. Data were collected through concept understanding test and self-efficacy questionnaire. The results showed that students\u27 concept understanding and self-efficacy belonged to the medium and low classes. However, there was a practically insignificant correlation between the two aspects. The implication is the importance of developing learning strategies that can improve students\u27 concept understanding and self-efficacy in the context of mathematics education.Pemahaman konsep dan self-efficacy merupakan dua aspek penting dalam pembelajaran matematika yang saling terkait. Namun masih terdapat perdebatan mengenai hubungan antara kedua aspek ini dalam konteks pembelajaran matematika. Oleh karena itu, penelitian ini dilakukan untuk menganalisis klasifikasi pemahaman konsep dan self-efficacy menggunakan K-means clustering dengan sampel siswa kelas VIII dari tiga sekolah terpilih di Kecamatan Wolowaru dan Kecamatan Kelimutu, Kab. Ende, NTT. Data dikumpulkan melalui tes pemahaman konsep dan angket self-efficacy. Hasil penelitian menunjukkan bahwa pemahaman konsep dan self-efficacy siswa termasuk dalam kelas sedang dan rendah. Namun korelasi yang tidak signifikan secara praktis antara kedua aspek tersebut. Implikasinya adalah pentingnya pengembangan strategi pembelajaran yang dapat meningkatkan pemahaman konsep dan self-efficacy siswa dalam konteks pendidikan matematik
Comparison Predictions of the Demam Berdarah Dengue (DBD) using Model Exponential Smoothing: Pegel’s Classification and ChatGPT
Get PDFThe evolution of AI since the Covid-19 pandemic has developed very rapidly. Until 2023, AI is claimed to be a threat to several professional jobs, especially data analysts and scientists. The purpose of this research is to check the effectiveness chat-GPT to predict about demam berdarah dengue (DBD) case. Method of the analyzing the data in this research is Mixed method. Quantitative method using exponential smoothing: pegel’s classification and qualitative method using GPT-3. The aim of this research is to check whether ChatGPT can predict the demam berdarah dengue (DBD) data time series. The prediction result are check it by exponential smoothing: pegel’s classification method. The benefit of this research is it can be used to reference how far the evolution of AI can be threaten the profession of data analyst or data scientist. The result of this study conclude that the ChatGPT (GPT-3) can’t predict DBD’d data correctly
Bahasa Indonesia
No full textInternship is part of a job training system that is held in an integrated manner between training at training institutions by working directly under the guidance and supervision of instructors or more experienced workers/laborers, in the process of producing goods and / or services in the company, in order to master certain skills or expertise. The internship program is part of the Merdeka Belajar Kampus Merdeka (MBKM) program, which provides opportunities for students from various universities in Indonesia in coordination with the ministry of education, culture, research, and technology (Kemendikbudristek) to learn in the world of work. The object in this study was focus on a student of the Statistics Study Program at Pattimura University. The purpose of this study is to model SEM-PLS based on cases from the results of questionnaire analysis, determine indicator variables that are feasible to be used as an influence on latent variables based on the SEM-PLS method, and identify the influence of exogenous latent variables, namely Motivation, Value Perception of Internship Program. SEM is one of the Multivariate data analysis methods which is a statistical analysis method to analyze several variables simultaneously. Based on the results and discussion in this study is modeling the influence of motivation, Perception of Internship Program Value, Perception of Self-Ability, and Perception of Specific Support for Student Interest resulting in the following structural equations:. These results are valid, reliable, and have been evaluated both through reflective and formative measurement processes
Hopf Bifurcation in a Modified Leslie-Gower Two Preys One Predator Model and Holling Type II Functional Response with Harvesting and Time-Delay
Get PDFIn this paper, a modified Leslie-Gower two preys one predator model and Holling type II functional response with harvesting and time-delay were discussed. Model analysis is carried out by determining fixed points, then analyzing the stability of the fixed points and discussing the existence of the Hopf bifurcation. In some conditions that occur in nature indicate the occurrence of hunting of prey and predator species by humans. Therefore, this model is modified by adding the assumption that prey and predators are being harvested. Another modification given to the model is the use of time delays.The delay time term is for taking into account the case that the members of the predator species need time from birth to predation for being active predators. The first case is a model without time delay, it is obtained that 3 fixed points are unstable and 7 fixed points are stable. One of them is the interior fixed point tested with the Routh-Hurwitz criteria. The second case is a model with a delay time, the critical delay value is obained. Hopf bifurcation occurs when the delay time value is equal to the critical delay value and also fulfills the transversality condition. Observations on the model simulation are carried out by varying the value of the delay time. When the Hopf bifurcation occurs, the graph on the solution plane shows a constant oscillatory movement. If the value of the delay time given is less than the critical value of the delay, the controlled system solution goes to a balanced state. Then when the delay time value is greater than the critical delay value, the system solution continues to fluctuate causing an unstable system condition