Jurnal Matematika, Statistika dan Komputasi
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PERAMALAN DATA DERET WAKTU MENGGUNAKAN TRANSFORMASI WAVELET DISKRIT HAAR
No full textDiscrete Wavelet Transform is a data transformation method that represents data in the time domain and frequency domain. This transformation appears to overcome the weakness of the Fourier transform which is only able to provide one domain information and is limited to certain windowing . The type of wavelet used is the Haar Wavelet. Identification of data periodicity using Periodogram analysis with Fisher\u27s Test statistics. The transformed data is decomposed into two components, namely the Approximation Coefficient and the Detail Coefficient. Both components are predicted using the Box-Jenkins ARIMA method. Model selection was carried out using the Akaike Information Criterion (AIC ) and Mean Square Error (MSE) methods . The forecast obtained is then reconstructed into the time domain (inverse). The application of the ARIMA model through wavelet transformation to Makassar City Air Humidity data for the period September 2006 - December 2012 shows that forecasting on the Approximation Coefficient obtained by the ARIMA model (0,0,3) with AIC = 112.2142 and MSE = 29.673. While forecasting on Detailed Coefficients is obtained by the ARIMA model (2,1,0) with AIC = 89.2 and MSE = 15,989.Transformasi Wavelet Diskrit merupakan metode transformasi data yang merepresentasikan data dalam domain waktu dan domain frekuensi. Transformasi ini muncul untuk mengatasi kelemahan transformasi Fourier yang hanya mampu memberikan satu informasi domain saja dan terbatas pada windowing tertentu. Jenis wavelet yang digunakan yaitu Wavelet Haar. Identifikasi keperiodikan data menggunakan analisis Periodogram dengan statistik Uji Fisher. Data hasil transformasi didekomposisi menjadi dua komponen yaitu koefisien Aproksimasi dan Koefisien Detail. Kedua komponen tersebut diramalkan menggunakan metode ARIMA Box-Jenkins. Pemilihan model dilakukan menggunakan metode Akaike Information Criterion (AIC) dan Mean Square Error (MSE). Peramalan yang diperoleh kemudian dikonstruksi kembali ke domain waktu (invers). Aplikasi model ARIMA melalui transformasi wavelet pada data Kelembaban Udara Kota Makassar periode September 2006 - Desember 2012 menunjukkan bahwa peramalan pada Koefisien Aproksimasi diperoleh model ARIMA (0,0,3) dengan nilai AIC = 112.2142 dan MSE=29.673 . Sementara peramalan pada Koefisien Detail diperoleh model ARIMA (2,1,0) dengan AIC = 89.2 dan MSE=15.989
PENDUGAAN FAKTOR – FAKTOR YANG MEMENGARUHI KASUS STUNTING DI JAWA BARAT TAHUN 2021 MENGGUNAKAN REGRESI SPASIAL BINOMIAL NEGATIF
Get PDFStunting is a childhood growth and development disorder characterized by below-normal height. West Java, with its stunting rate of 24.5 percent, is one of the provinces included in the top 12 priority provinces in implementing the National Action Plan to Accelerate Stunting. Stunting cases are count data and their occurrence is rare. The analysis for the count data is Poisson regression with the assumption that equidispersion must be met. One way to overcome overdispersion is to use negative binomial regression. This study aimed to determine predictors/factors affecting stunting cases in West Java province in 2021 using negative binomial spatial regression. The data in this study comes from the publication of the West Java Health Service and the West Java Central Statistics Agency in 2021 with districts/cities as the object of observation. There is a spatial effect in the stunting data, so the spatial regression model is suitable. The results show that there is an overdispersion in the Poisson regression. The spatial effect test shows that there is a spatial dependence on the response variable and some predictors. The negative spatial autoregressive binomial is the best model with the lowest AIC value. The factors that have a significant effect are the percentage of infants aged less than six months who are breastfed, the percentage of food processing establishments that meet the requirements, and the percentage of infants with low birth weight.Stunting adalah gangguan tumbuh kembang anak yang ditandai dengan tinggi badan di bawah normal. Jawa Barat dengan angka stunting sebesar 24,5 persen merupakan salah satu provinsi yang masuk dalam 12 besar provinsi prioritas dalam pelaksanaan Rencana Aksi Nasional Percepatan Stunting. Kasus stunting merupakan data hitungan dan jarang terjadi. Analisis untuk data cacahan adalah regresi Poisson dengan asumsi equidispersi harus terpenuhi. Salah satu cara untuk mengatasi overdispersi adalah dengan menggunakan regresi binomial negatif. Penelitian ini bertujuan untuk mengetahui prediktor/faktor yang mempengaruhi kasus stunting di Provinsi Jawa Barat tahun 2021 dengan menggunakan regresi spasial binomial negatif. Terdapat efek spasial pada data stunting, sehingga model regresi spasial cocok digunakan. Hasilnya menunjukkan bahwa ada overdispersi pada regresi Poisson. Uji efek spasial menunjukkan adanya ketergantungan spasial pada variabel respon dan beberapa prediktor. Binomial autoregresif spasial negatif adalah model terbaik dengan nilai AIC terendah. Faktor yang berpengaruh nyata adalah persentase bayi usia kurang dari enam bulan yang mendapat ASI, persentase tempat pengolahan makanan yang memenuhi syarat, dan persentase bayi dengan berat badan lahir rendah
Grup dan Isomorfisma Grup pada Pyraminx
Get PDFPyraminx is a twisty puzzle in the shape of a tetrahedron with 4 sides. Pyraminx is played with the bottom completely flat and the front side facing the person holding the Pyraminx. The goal of the Pyraminx game is to randomize the colors, then return the scrambled colors to their original color positions by rotating the sides. This research does not discuss the most effective way of solving Pyraminx but focuses more on proving that movements in Pyraminx form group and that there is a group isomorphism from the group of Pyraminx movements to the symmetry permutation subgroup in Pyraminx. First, it is proved that movements in Pyraminx form group using 2 methods, namely direct proof in Pyraminx (Pyaminx movement group) and performing permutations in set containing numeric labels in the form of numbers 1 to 36 on Pyraminx facets by following the movements of Pyraminx ( symmetry permutation subgroup). Furthermore, it is proved that there is a group isomorphism from the Pyraminx movement group to the symmetry permutation subgroup in Pyraminx
Path Analysis of Influence of Economic and Social Factors on the Human Development Index in South Sulawesi in 2022
Get PDFThe Human Development Index (HDI) serves as an indicator for assessing socio-economic development in a region. Each area strives to improve its HDI by considering the factors that influence it in that specific region. This research aims to identify the direct and indirect influences of economic and social factors, such as Life Expectancy (LE), Gross Regional Domestic Product per capita (GRDPpc), Labor Force Participation Rate (LFPR) through Average Years of Schooling (AYS) on the HDI in South Sulawesi in 2022. The data used in this study are secondary data obtained from the Central Statistics Agency (BPS) of South Sulawesi Province in 2022. The method applied in this research is a path analysis that examines the relationships between variables, both direct and indirect influences. The research results show that in the equation of sub-structure 1, LE and GRDP per capita ADHB have a direct influence on AYS, while LFPR does not have a direct impact on AYS. The magnitude of the influence of variables in sub-structure 1 is 53%. In the equation of sub-structure 2, LE, GRDP per capita ADHB, LFPR, and AYS have a significant direct impact on HDI. Additionally, LE and GRDP per capita ADHB have an indirect influence through AYS on HDI. The magnitude of the influence of variables in sub-structure 2 is 93.5%. Therefore, the variables that have both direct and indirect effects on HDI through AYS are LE and GRDP per capita ADHB
Model Matematika Penyebaran Covid-19 Dengan Karantina Dan Vaksinasi
Get PDFAbstract
We present a mathematical model of COVID-19 disease by modifying the SEIR model. The model considers two additional compartments, quarantine (Q) and vaccination (V) which aim to control the spread of COVID-19. Based on the model, we obtained a disease-free equilibrium point and an endemic equilibrium point. The basic reproduction numbers were calculated using the next-generation matrix method. In this model, we analyzed the stability conditions that must be satisfied by the defining parameters. We perform data on the spread of COVID-19 in Indonesia for estimation to provide the parameter value in the model. Based on the result, there is an influence of changes in several parameter values on the number of individuals infected with COVID-19.
Abstrak
Dalam penelitian ini, diberikan model matematika penyebaran penyakit COVID-19 dengan memodifikasi model SEIR. Model yang digunakan mempertimbangkan dua kompartemen tambahan yaitu karantina (Q) dan vaksinasi (V) sebagai usaha untuk mengendalikan penyebaran COVID-19. Berdasarkan model yang telah dibangun, diperoleh titik kesetimbangan bebas penyakit dan titik kesetimbangan endemik. Nilai bilangan reproduksi dasar dihitung dengan menggunakan metode matriks next generation. Dalam model ini juga diperoleh syarat kestabilan yang harus dipenuhi oleh parameter yang telah didefinisikan. Data penyebaran COVID-19 di Indonesia digunakan untuk memberikan estimasi nilai parameter pada model. Berdasarkan analisa yang diperoleh, terdapat pengaruh dari perubahan beberapa nilai parameter terhadap jumlah individu terinfeksi COVID-19.
 
Dimensi Metrik dari Hasil Operasi Shackle Graf Siklus C_3
No full textLet G be a connected graph and W be a ordered vertices subset on a connected graph . The set W is called resolving set for G if every vertex on graph G has distinct representation of W. A resolving set containing a minimum number of vertices is called resolving set minimum or basis for G and the cardinality of resolving set is the metric dimension on graph G, denoted by dim(G). In the thesis discusses about metric dimensions of shackle operation C3 cycle graph, dim(Shack(C31,C32,…,C3k:v31=v12,v32=v13,…,v3k-1=v1k ))=2 for k>=2 . To proof this results, we was used mathematical induction method.Misalkan G adalah graf terhubung dan W adalah sub himpunan titik terurut pada graf terhubung G. Himpunan W disebut himpunan pembeda pada G jika untuk setiap titik pada graf G memiliki representasi jarak yang berbeda tehadap W. Himpunan pembeda dengan banyak anggota minimum disebut himpunan pembeda minimum atau basis dari G dan kardinalitas himpunan tersebut adalah dimensi metrik pada graf G, dinotasikan dengan dim(G). Dalam makalah ini dibahas mengenai dimensi metrik hasil operasi shackle graf siklus C3, dim(Shack(C31,C32,…,C3k:v31=v12,v32=v13,…,v3k-1=v1k ))=2 untuk k>=2. Metode yang digunakan dalam membuktikan hasil tersebut adalah induksi matematika
Modeling of COVID-19 Cases in Indonesia with the Method of Geographically Weighted Regression
Get PDFThe COVID-19 pandemic has spread to all corners of the world, including Indonesia. Various factors affect the spread of COVID-19 cases in an area so that the government and the community can make prevention and control efforts so that this pandemic does not spread. This study aims to model the number of COVID-19 cases in Indonesia using the Geographically Weighted Regression (GWR) method, which develops a linear regression model. The GWR model uses weights based on the location of each observation so that the model is obtained for that location. Determine the weighting on the bandwidth. Optimum bandwidth selection is obtained by minimizing the value of Cross-Validation (CV). The GWR model using a fixed bisquare kernel weighting function has an optimum bandwidth of 0.999948 with a minimum CV value of 397.076.128 with a coefficient of determination R2 of 85.1 %. The results show that the number of positive cases positively correlates with the number of patients who died from COVID-19. In contrast, the number of recovered patients negatively correlates with the number of patients who died from COVID-19
Global Stability of Covid-19 Disease Free Based on Sivrs Model
Get PDFThis study discusses the spread of the Covid-19 disease by including new variant variables. The model used by SIVRS assumes there are deaths caused by Covid-19 and the new variant Covid-19. In addition, individuals who have been infected with the new variant of Covid-19 can recover. Based on the model, disease-free equilibrium points and endemic equilibrium points are obtained. The analysis was carried out around the disease-free equilibrium point and the result was that the global asymptotically stable disease-free equilibrium point with the condition R0<1. Furthermore, a simulation was carried out with the Maple 18.Penelitian ini membahas mengenai penyebaran penyakit Covid-19 dengan menyertakan variabel varian baru. Model yang digunakan SIVRS dengan asumsi terdapat kematian yang disebabkan oleh Covid-19 dan Covid-19 varian baru. Selain itu, individu yang telah terinfeksi Covid-19 varian baru dapat sembuh. Berdasarkan model, diperoleh titik ekuilibrium bebas penyakit dan titik ekuilibrium endemik. Analisa dilakukan disekitar titik ekuilibrium bebas penyakit diperoleh hasil bahwa titik ekuilibrium bebas penyakit stabil asimtotik global dengan syarat R0<1. Selanjutnya dilakukan simulasi dengan program Maple 18
ANALISIS PENGELOMPOKAN DERAJAT KESEHATAN IBU DAN ANAK DI INDONESIA MENGGUNAKAN STRUCTURAL EQUATION MODELING PARTIAL LEAST SQUARE-PREDICTION ORIENTED SEGMENTATION (SEM PLS-POS)
Get PDFOne of Indonesia\u27s development goals in 2020-2024 is to form quality and competitive human resources. One of the efforts to achieve this goal is to improve the quality of maternal and child health. However, the issue of Maternal and Child Health (MCH) is still a challenge for the Indonesian health system. This study aims to determine the modeling and to obtain provincial groupings based on the degree of maternal and child health in Indonesia. The method used is Structural Equation Modeling Partial Least Square-Prediction Oriented Segmentation (SEM PLS-POS). The results of the PLS SEM analysis showed that the environmental variables and health services had a significant effect on the health status of mothers and children with an R2 value of 48.8%. The grouping of provinces based on the degree of maternal and child health in Indonesia using PLS-POS produces 3 segment classes. Segment 1 consists of 11 provinces, segment 2 consists of 13 provinces and segment 3 consists of 10 provinces with a large influence between different latent variables
Regresi Logistik Multinomial untuk Memodelkan Kombinasi antara Status IPKM dan Status IPM Kabupaten/Kota di Pulau Kalimantan
Get PDFMultinomial Logistics Regression (MLR) is a regression model developed from the Binary Logistics Regression (BLR) model. The response variable of the RLM model has three or more categories and has a multinomial distribution, with the data scale being nominal. The response variable in this study is a combination of the Public Health Development Index (PHDI) status and the Human Development Index (HDI) status of districts/cities in Kalimantan Island, 2018, divided into four categories with category one as a comparison. The predictor variables used were the number of the public health center, the percentage of poor people, economic growth, the pure junior high school participation rate, and the percentage of the population with a minimum of junior high school education. The MLR parameter model was estimated using the Maximum Likelihood Estimation (MLE) method and Newton-Raphson iteration. The hypothesis testing of the MLR model was used by the Likelihood Ratio Test (LRT) method and the Wald test. The best model selection in this study uses the backward method, and the interpretation of the best MLR model uses the odds ratio value. The results showed that the best MLR model is a model that has three predictor variables. The factors that significantly influenced the combination of PHDI status and the HDI status of districts/cities in Kalimantan Island in 2018 were the percentage of poor people, economic growth, and the percentage of people with the minimum level of education in junior high school.Regresi Logistik Multinomial (RLM) merupakan model regresi yang dikembangkan dari model Regresi Logistik Biner (RLB). Variabel respon model RLM mempunyai tiga atau lebih kategori dan berdistribusi multinomial dengan skala datanya adalah nominal. Variabel respon dalam penelitian yaitu kombinasi antara status Indeks Pembangunan Kesehatan Masyarakat (IPKM) dan status Indeks Pembangunan Manusia (IPM) kabupaten/kota di pulau Kalimantan tahun 2018 yang terbagi dalam empat kategori dengan kategori satu sebagai pembanding. Variabel prediktor yang digunakan yaitu jumlah puskesmas, persentase penduduk miskin, pertumbuhan ekonomi, angka partisipasi murni SMP, dan persentase penduduk yang berpendidikan minimal SMP. Penaksiran parameter model RLM dilakukan dengan menggunakan metode Maximum Likelihood Estimation (MLE) dan iterasi Newton-Raphson. Pengujian hipotesis parameter model RLM menggunakan metode Likelihood Ratio Test (LRT) dan uji Wald. Pemilihan model terbaik dalam penelitian ini menggunakan metode backward dan interpretasi model RLM terbaik menggunakan nilai odds ratio. Hasil penelitian menunjukkan bahwa model RLM terbaik adalah model yang mempunyai tiga variabel prediktor. Faktor-faktor yang berpengaruh signifikan terhadap kombinasi antara status IPKM dan status IPM kabupaten/kota di pulau Kalimantan tahun 2018 adalah persentase penduduk miskin, pertumbuhan ekonomi, dan persentase penduduk yang berpendidikan minimal SMP