Jurnal Matematika, Statistika dan Komputasi
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Parameter Estimation of Zero Inflated Bivariate Ordered Probit Model with Berndt, Hall, Hall, and Hausman Iteration Approach
Full text linkProbit regression is a statistical analysis method used to analyze the relationship between response variables and predictor variables where the response variable is categorical with a normal distribution link function. Based on the measurement scale, probit regression is divided into two, namely binary probit regression and ordinal probit regression. Based on the number of response variables, ordinal probit regression is divided into two, namely univariate ordinal probit regression and multivariate ordinal probit regression. Multivariate ordinal probit regression that has two response variables is called bivariate ordinal probit regression. In univariate ordinal regression, if there are many unequal proportions in certain categories, conventional univariate probit ordinal regression cannot provide good estimation results. Therefore, univariate ordinal probit regression must be developed into Zero Inflated Ordered Probit (ZIOP) Regression. Similar to univariate ordinal probit regression, bivariate ordinal probit regression produces poor estimates if the response variable is zero inflated, so it is developed into Zero Inflated Bivariate Ordered Probit Regression (ZIBOPR). This study aims to estimate the parameters of the ZIBOPR model, using the Maximum Likelihood Estimator (MLE) method with Brendt, Hall, Hall, and Hausman (BHHH) numerical iteration. This study produces a parameter estimator of the ZIBOPR model, which is a combination of binary probit regression and bivariate ordinal probit regression with the BHHH numerical iteration approach
Linearized Ridge Regression Modeling with MM-Estimator in Statistical Downscalling for Rainfall Forecasting
Full text linkRainfall is one of the important climate variables to be predicted because it affects various sectors, such as agriculture, health, and disasters. One method that can be used to forecast rainfall is statistical downscaling, which is the process of relating large-scale climate variables to local-scale climate variables. However, this method has several challenges, such as the presence of heteroscedasticity, multicollinearity, and outliers in the data. To overcome these challenges, this study proposes linearized ridge regression modelling with MM-estimator in statistical downscaling for rainfall forecasting. Linearized ridge regression is a linear regression method that can reduce the influence of multicollinearity by adding a penalty parameter to the covariance matrix. MM-estimator is a robust method that can handle outliers by using two estimators, namely the initial estimator (S-estimator) and the final estimator (M-estimator). This research uses daily rainfall data from BMKG Pangkep station and Global Circulation Model (GCM) output data as predictors. The results showed that linearized ridge regression modelling with MM-estimator has better performance than linearized ridge regression modelling without MM-estimator in terms of accuracy and resilience to outliers with a correlation value of 0.94 against the acute rainfall data, the Root Means Square Error value obtained is 97.26 and 86.57% of determinant coefisient value. Therefore, linearized ridge regression modelling with MM-estimator can be used as an alternative statistical downscaling method for rainfall forecasting. Based on the forecasting results for January - December 2023, it shows that the highest rainfall in Pangkep Regency is in January and the lowest rainfall is in September
The Fuzzy-Possibilistic Product Partition c-Means (FPPPCM) algorithm for Clustering the Welfare Levels of Regencies in East Java
Full text linkWelfare is a condition where society is free from deviant behavior, poverty, ignorance, and fear, thus allowing individuals to obtain a safe and peaceful life. East Java is among the provinces in Indonesia that recorded the highest incidence of poverty from 2013 to 2022; however, it has also demonstrated a consistent decline in the number of individuals living in poverty during this period. This study aims at applying the Fuzzy-Possibilistic Product Partition c-Means (FPPPCM), which combines the probabilistic approach of Fuzzy c-Means and the possibilistic approach of Possibilistic c-Means, and is effective in handling outliers, to clustering the welfare levels of regencies and cities in East Java. The exploration is based on the data of the Badan Pusat Statistik (BPS) for 2024. Based on clustering the welfare levels, the following are the end results of the study: Cluster 1 (low population, high education/life expectancy but low labor participation and high poverty line, i.e. Kediri City) may find aid in programs that work on the issues like job creation, affordable housing, and family planning outreach to reduce inequality. Cluster 2 (medium population, low education/expenditure but high labor participation/home ownership, i.e. Pacitan) could promote vocational training, poverty reduction through SME support, and give education to the workforce. Cluster 3 (high population, low life expectancy, medium indicators but high family planning, i.e. Lamongan) should focus on improvement of the healthcare infrastructure, the health of the mother and child, and creation of industrial jobs for the local peopl
Simulasi Pemodelan Dampak Pengobatan yang Tidak Lengkap pada Penyebaran Tuberkulosis
Full text linkAmong the most common diseases globally is tuberculosis (TB). The spread dynamics of TB are formulated in the form of a mathematical model with five subpopulation densities, namely, susceptible individuals, latent individuals, TB active individuals, treated individuals, and recovered individuals. The existence of an equilibrium point is contingent upon the value of the basic reproduction number Ro. Ro is a key metric for understanding the potential for disease transmission and is obtained from the next generation matrix. Stability analysis for TB models is investigated by determining the criteria for the local stability of equilibrium points. After that, a sensitivity analysis is conducted to identify TB model parameters that most affect Ro value. The solution behavior of the TB model is shown by graphs generated numerically with the Runge-Kutta fourth-order method and Matlab softwareSalah satu kasus penyakit menular terbanyak di dunia adalah tuberkulosis (TB). Dinamika penyebaran TB dinyatakan dalam bentuk model matematika dengan lima kepadatan subpopulasi, yaitu individu rentan, individu laten, individu TB aktif, individu yang diobati, dan individu sembuh. Keberadaan titik kesetimbangan memiliki syarat batas bilangan reproduksi dasar . R0 merupakan metrik utama untuk memahami potensi penularan penyakit dan diperoleh dari matriks generasi selanjutnya. Analisis kestabilan untuk model TB diselidiki dengan menentukan syarat kestabilan lokal titik kesetimbangan. Kemudian analisis sensitivitas dilakukan untuk mengidentifikasi parameter-parameter dalam model TB yang paling berpengaruh terhadap nilai R0. Perilaku solusi model TB ditunjukkan dengan grafik yang dihasilkan secara numerik menggunakan metode Runge-Kutta orde 4 dan software Matlab
Hopf bifurcation in a dynamic mathematical model in facultative waste stabilization pond
Full text link In this paper, we discuss the predator-prey model using Holling type II functional response with the time delay in facultative stabilization pond. In this research, we discuss the predator-prey model using Holling type II functional response with the time delay, determining the equilibrium point, the stability analysis of predator-prey model using Holling type II functional response with the time delay and numerical simulation of the predator-prey model using Holling type II functional response with the time delay. The method used to analyse the problem is by literature study. The steps used are the development of a mathematical model of change of dissolved oxygen concentration, phytoplankton and zooplankton, mathematical equation solving algorithm, field data, simulation using Maple and Mathematica 9 software and validation with research
On 2-Primal Quinary Semiring and its Characterizations by Special Subsets
Full text linkIn this research, we introduce a new concept of 2-primal quinary semiring and its characterizations by utilizing special subsets. This concept is a generalization of 2-primal ternary semiring. The method of this research is a literature study on scientific articles in international journals. This research starts from concept of quinary semiring and some its ideals, then continues by studying the basic concept of 2-primal quinary semiring, including weakly and strongly nilpotent sets. Next, we define some special subsets of quinary semiring, and then provide some of their properties. Through this special subsets, we provide characterizations of 2-primal quinary semiring
Numerical Simulation and Convergence of Variational Iteration Method on Kuramoto-Sivashinsky Equation
Full text linkPartial differential equations (PDEs) are a useful tool for modelling a variety of mathematical problems, including those in the field of mathematical physics. The Kuramoto–Sivashinsky (K-S) equation is one type of partial differential equation (PDE). A numerical approach is necessary to achieve a solution since not all partial differential equations (PDEs) can be solved analytically in reality. Similar to the K-S equation, this equation cannot be solved without the use of a numerical technique. Variational Iteration Method (VIM) is one of the techniques used to solve the K-S problem. Three core ideas form the basis of the Variational Iteration Method (VIM): the generalized Lagrange multiplier, finite variation and correction function. The aforementioned three basic concepts can be employed in the formulation of the iteration formula. The objective of this research is to implement the VIM numerical scheme on the K-S equation. A wave-shaped graph is obtained based on the K-S equation, which has one valley and two hills, starting with the solution at when As increases, the solution value decreases and reaches a minimum at when . Subsequently, the curve ascends once more, crossing the -axis and reaching a maximum valueEven though just a small number of iterations are carried out, the Variational Iteration approach is successful in obtaining correct answers, according to the convergence analysis of the method on the K-S problem. It can be concluded that VIM is an appropriate and efficacious instrument for the resolution of equations of the K-S variety. It may be employed as a method of solution exploration and as a verification tool for the exact solution
Topological Index of Coprima Graph of Integers Group Modulo with Order of Prime Power
Full text linkThis paper explores the topological indices of the coprime graph defined on the group of integers modulo a prime power. A coprime graph is constructed with vertices representing group elements, where two vertices are adjacent if and only if their orders are relatively prime. The study focuses on analyzing four topological indices: the ABC index, Forgotten index, Gourava index, and Nirmala index. This work aims to enhance the understanding of the topological properties of coprime graphs within the structure of integer modulo groups of prime power order
Implementation of Singular Spectrum Analysis Method for Prediction of Average Sunshine Duration
Full text linkSolar irradiance is the process by which radiant energy from the sun reaches the earth. BMKG states that solar irradiance reaches 100% when the sun shines for 8 hours a day. Less than 8 hours of solar irradiance a day can affect local and global climate systems. This research aims to analyze and predict of average sunshine duration in Pasuruan with the Singular Spectrum Analysis (SSA) method. Based on the SSA model for optimal solar irradiation with and Grouping Effect , this study analyzes the prediction of average sunshine duration in Pasuruan which produces a Mean Absolute Percentage Error (MAPE) value of 19.53%. The results indicate that the predictions are effectively categorized for estimating the average solar irradiance. The highest average was in July at 60.1% and the lowest average was in November at 12.82%
Block Backward Differentiation Formula Method for Solving Van der Pol Equation
Full text linkThe Van der Pol equation is often used as a basic model for oscillatory systems in physics and biology, such as the interaction of two plates on geological faults as well as oscillations in various electrical and electronic systems. The Van der Pol equation is a second-order nonlinear differential equation known to have stiffness properties, especially for large values of the μ parameter. This study aims to develop the Block Backward Differentiation Formula method that is applied in a block manner to solve the Van der Pol equation that is reduced to a system of first-order differential equations. This method is proven to be effective for solving Van der Pol equation with various values of μ parameter, although it requires a fairly small step size to achieve convergence at larger values of μ parameter. The resulting solutions are close to the results provided by Matlab solvers, namely ODE45 and ODE15