Penelitian ini mengembangkan model penyebaran penyakit tuberkulosis menggunakan model SIR yang ditambahkan dengan faktor penggunaan masker medis. Pembentukan model diawali dengan membuat diagram kompartemen alur penyebaran penyakit tuberkulosis melalui kontak antar individu dengan menggunakan masker medis. Kemudian dibentuk sistem persamaan diferensial nonlinear berdasarkan diagram kompartemen tersebut. Berdasarkan sistem tersebut, dicari titik ekuilibrium bebas penyakit, titik ekuilibrium endemik, dan bilangan reproduksi dasar (R0). Analisis kestabilan titik ekuilibrium bebas penyakit menggunakan linierisasi dan titik ekuilibrium bebas penyakit yang diperoleh bersifat stabil asimtotik saat (R0<1) . Simulasi model dilakukan dengan nilai-nilai parameter yang diambil dari beberapa jurnal dan mengambil kasus di kota Makasar. Hasil simulasi menunjukkan bahwa nilai (R0<1). Hal ini berarti bahwa penyakit tuberkulosis dalam waktu mendatang akan menghilang. Namun jika nilai parameter penggunaan masker medis dikurangi dan nilai parameter kontak penyebaran penyakit tuberkulosis dinaikkan, maka nilai (R0>1). Hal ini berarti penyakit tuberkulosis akan menjadi endemik.
Wind speed is one of the most important weather factors in the landing and takeoff process of airplane because it can affect the airplane's lift. Therefore, we need a model to predict the wind speed in an area. In this research, the wind speed forecast using the ARIMA model is discussed which has differencing parameters in the form of fractions. This model is called the ARFIMA model. In estimating differencing parameters two methods are considered, namely parametric and semiparametric methods. Exact Maximum Likelihood (EML) is used under parametric method. Meanwhile, four methods semiparametric estmation are used, i.e Geweke and Porter-Hudak (GPH), Smooth GPH (Sperio), Local Whittle and Rescale Range (R/S). The result shows the best estimation method is GPH with the selected model is ARFIMA (2,0.334,0).Keywords: ARFIMA, Parametric Method, Semiparametric Method. AbstrakKecepatan angin merupakan salah satu faktor cuaca yang penting dalam proses pendaratan dan tinggal landas pesawat karena dapat mempengaruhi daya angkat pesawat. Oleh karena itu, diperlukan suatu model untuk memprakirakan kecepatan angin di suatu wilayah. Artikel ini membahas prakiraan kecepatan angin dengan menggunakan model ARIMA yang memiliki parameter differencing berupa bilangan pecahan. Model ini disebut model ARFIMA. Pada estimasi parameter differencing terdapat dua metode yang digunakan pada penelitian ini, yaitu metode parametrik dan metode semiparametrik. Metode parametrik yang digunakan adalah Exact Maximum Likelihood (EML) dan empat metode semiparametrik yang digunakan adalah Geweke and Porter-Hudak (GPH), Smooth GPH (Sperio), Local Whittle dan Rescale Range (R/S). Hasil analisis menunjukkan pada kasus ini metode estimasi terbaik adalah GPH dengan model terpilih adalah ARFIMA(2,0.334,0).Kata kunci: ARFIMA, Metode Parametrik, Metode Semiparametrik.
This research discusses determination of the best route for the goods distribution from one depot to customers in various locations using the Capacitated Vehicle Routing Problem with Time of Windows (CVRPTW) model with a goal programming approach. The goal function of this model are minimize costs, minimize distribution time, maximize vehicle capacity and maximize the number of customers served. We use case study in CV. Oke Jaya companies which has 25 customers and one freight vehicle with 2000 kg capacities to serve the customers in the Serang, Pandeglang, Rangkasbitung and Cikande. For simulation we use software LINGO. Based on this CVRPTW model with a goal programming approach, there are four routes to distribute goods on the CV. Oke Jaya, which considers the customer’s operating hours, with total cost is Rp 233.000,00, the total distribution time is 17 hours 57 minutes and the total capacity of goods distributed is 6150 kg.
Likert-type scale data are ordinal data and are commonly used to measure latent constructs in the educational, social, and behavioral sciences. The ordinal observed variables are often treated as continuous variables in factor analysis, which may cause misleading statistical inferences. Two robust estimators, i.e., unweighted least square (ULS) and diagonally weighted least square (DWLS) have been developed to deal with ordinal data in confirmatory factor analysis (CFA). Using synthetic data generated in a Monte Carlo experiment, we study the behavior of these methods (DWLS and ULS) and compare their performance with normal theory-based ML and GLS (generalized least square) under different levels of experimental conditions. The simulation results indicate that both DWLS and ULS yield consistently accurate parameter estimates across all conditions considered in this study. The Likert data can be treated as a continuous variable under ML or GLS when using at least five Likert scale points to produce trivial bias. However, these methods generally fail to provide a satisfactory fit. Empirical studies in the field of psychological measurement data are reported to present how theoretical and statistical instances have to be taken into consideration when ordinal data are used in the CFA model.Keywords: confirmatory factor analysis, diagonally weighted least square, generalized least square, Likert data, maximum likelihood.
This research discusses the calculation of the premium of term life-insurance based on sharia principles. The difference between the conventional method and the sharia principle is in the concept of interest rates. In this research, the concept of interest in the conventional method is replaced by the Return on Investment (ROI) that changes stochastically following the Langevin type model. The Monte-Carlo simulation is applied to generate the ROI with some initial values. On the mechanism of premium management, we apply the system without a saving element and the Al-Mudharabah relationship where the participants will get a sharing-profit of the operating surplus if they don’t make a claim until the end of the agreement period. We assume that the administrative expenses only charged in the first year. Therefore, the operating surplus will be greater after the first year. In addition, we do 20 times of Monte–Carlo simulations to generate the ROI with initial value are 7.5%, 9%, and 10%. The result shows that the annual premiums become smaller when the ROI become greater and vice versa. This is because the company get a smaller return when the initial of ROI is small. So the annual premium will be greater. The annual premium for male participants is greater than women because the rate of death of men is greater than women. The other factors that make the annual premium more expensive are length of the agreement and greater compensation.Keywords: Langevin type model, stochastic differential equation, system without a saving element, Al-Mudharabah principle, Monte–Carlo simulation. AbstrakPenelitian ini membahas mengenai perhitungan dana premi asuransi jiwa berjangka berdasarkan prinsip–prinsip syariah. Perbedaan antara metode konvensional dengan prinsip syariah adalah pada konsep tingkat bunga. Pada penelitian ini, konsep bunga digantikan dengan nilai Return on Investment (ROI) yang berubah secara stokastik mengikuti model tipe Langevin. Simulasi Monte–Carlo diterapkan untuk membangkitkan nilai ROI menggunakan beberapa nilai awal. Pada mekanisme pengelolaan dana premi, kami menerapkan sistem tanpa unsur tabungan dan hubungan Al-Mudharabah dimana peserta akan mendapatkan bagi hasil atas surplus operasional jika peserta tersebut tidak melakukan klaim sampai akhir masa perjanjian. Kami mengasumsikan bahwa biaya administrasi hanya dibebankan pada tahun pertama. Sehingga surplus operasional akan menjadi lebih besar setelah tahun pertama. Selain itu, kami melakukan 20 kali simulasi Monte–Carlo untuk membangkitkan ROI dengan nilai awal 7.5%, 9%, dan 10%. Hasil menunjukkan bahwa premi tahunan akan semakin kecil jika nilai awal dari ROI membesar dan sebaliknya. Hal ini disebabkan oleh keuntungan perusahaan yang kecil jika nilai awal ROI semakin kecil sehingga premi tahunan haruslah lebih besar. Premi tahunan untuk peserta laki-laki cenderung lebih besar daripada premi tahunan peserta wanita. Hal ini karena tingkat kematian laki-laki lebih tinggi daripada wanita. Faktor lain yang membuat premi tahunan lebih besar adalah lamanya masa kontrak asuransi dan kompensasi yang semakin besar.Kata kunci: Model tipe Langevin, persamaan diferensial stokastik, sistem tanpa unsur tabungan, prinsip Al-Mudharabah, simulasi Monte–Carlo.
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