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All Journal FORUM STATISTIKA DAN KOMPUTASI IPTEK The Journal for Technology and Science CAUCHY: Jurnal Matematika Murni dan Aplikasi Jurnal Hortikultura Journal of the Indonesian Mathematical Society JTAM (Jurnal Teori dan Aplikasi Matematika) Jambura Journal of Mathematics InPrime: Indonesian Journal Of Pure And Applied Mathematics SRIWIJAYA JOURNAL OF ENVIRONMENT Milang Journal of Mathematics and Its Applications MILANG Journal of Mathematics and Its Applications
I Wayan Mangku
Departemen Matematika, Fakultas MIPA, IPB University, Jawa Barat,
Agriculture, Biological Sciences & Forestry Computer Science & IT Control & Systems Engineering Earth & Planetary Sciences Energy Environmental Science Mathematics Public Health

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A Study on the Estimator Distribution for the Expected Value of a Compound Periodic Poisson Process with Power Function Trend Safitri, Nurul Indah; Mangku, I Wayan; Sumarno, Hadi
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 4, No 2 (2022)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15408/inprime.v4i2.25104

Abstract

This article discusses the estimation for the expected value, also called the mean function, of a compound periodic Poisson process with a power function trend. The aims of our study are, first, to modify the existing estimator to produce a new estimator that is normally distributed, and, second, to determine the smallest observation interval size such that our proposed estimator is still normally distributed. Basically, we formulate the estimator using the moment method. We use Monte Carlo simulation to check the distribution of our new estimator. The result shows that a new estimator for the expected value of a compound periodic Poisson process with a power function trend is normally distributed and the simulation result shows that the distribution of the new estimator is already normally distributed at the length of 100 observation interval for a period of 1 unit. This interval is the smallest size of the observation interval. The Anderson-Darling test shows that when the period is getting larger, the p-value is also getting bigger. Therefore, the larger period requires a wider observation interval to ensure that the estimator still has a normal distribution.Keywords: moment method; normal distribution; Poisson process; the smallest observation interval. AbstrakPada artikel ini dibahas tentang pendugaan fungsi nilai harapan Proses Poisson periodik majemuk dengan tren fungsi pangkat. Tujuan penelitian kami adalah, pertama, memodifikasi penduga yang telah ada untuk menghasilkan penduga baru yang memiliki distribusi normal. Kedua, menentukan ukuran interval pengamatan terkecil sehingga penduga yang diusulkan masih berdistribusi normal. Pada dasarnya, penduga yang kami usulkan diformulasi menggunakan metode momen. Kami menggunakan metode simulasi Monte Carlo untuk memeriksa sebaran distribusinya. Hasil menunjukkan bahwa penduga yang baru untuk fungsi nilai harapan Proses Poisson periodik majemuk dengan tren fungsi pangkat memiliki distribusi normal. Hasil simulasi menunjukkan bahwa penduga baru telah berdistribusi normal pada panjang interval pengamatan 100 untuk periode sebesar 1 satuan. Interval pengamatan ini merupakan ukuran interval pengamatan terkecil. Selain itu, hasil uji Anderson-Darling menunjukkan bahwa ketika periode semakin besar maka p-value juga semakin besar. Oleh karena itu, periode yang lebih besar memerlukan interval pengamatan yang lebih panjang untuk menjamin penduga yang kami usulkan tetap berdistribusi normal.Kata Kunci: metode momen; distribusi normal; proses Poisson; interval pengamatan terkecil. 2020MSC: 62E17 
M/M/1 Non-preemptive Priority Queuing System with Multiple Vacations and Vacation Interruptions Dillah Rismawati; I Wayan Mangku; Hadi Sumarno
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 3 (2023): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i3.14910

Abstract

Non-preemptive priority queue system is a type of priority queue where customers with higher priorities cannot interrupt low priority one while being served. High priority consumers will still be at the head of the queue. This article discusses the non-preemptive priority queue system with multiple working vacations, where the vacation can be interrupted. Customers are classified into two classes, namely class I (non-preemptive priority customers) and class II, with exponentially distributed service rates. Customers will still receive services at a slower rate than during normal busy periods when they enter the system while it is on vacation. Suppose other customers are waiting in the queue after completing service on vacation. In that case, the vacation will be interrupted, and the service rate will switch to the busy period service rate. The model's performance measurements are obtained using the complementary variable method and analyzing the state change equation following the birth and death processes to find probability generating function for both classes. The results of the numerical solution show that the expected value number of customers and waiting time of customers in the queue for both class customers will be reduced when the vacation times rate (θ) and the vacation service rate (μ_0 ) increase.
Comparing the Accuracy of Markov Switching – AR and Prophet Models in Predicting the Blue Bird Stock Prices Yulianty, Sherly; Mangku, I Wayan; Budiarti, Retno
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 2 (2025): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i2.30096

Abstract

One form of investment asset that is in high demand for profit is stocks. However, stock prices fluctuate, so a mathematical model is needed to model the movement and calculate stock price predictions. Stock price movements often form several groups (states) of change, so the Markov Switching Autoregressive (MS-AR) model can be used to model and calculate stock price predictions. In addition, stock price movements often contain trend and seasonal patterns, so the Prophet model can be used to model movements and calculate stock price predictions. In this study, the Prophet model is modified by generating random numbers that spread normally with parameter values obtained from the error value of the Prophet base model. This study aims to compare the performance of the MS-AR model with the Prophet model in predicting BIRD stock prices. This research is a quantitative study with secondary data in the form of BIRD stock closing price data for the period 11 February 2023 to 11 February 2024. In this study, two models, MS-AR and Prophet, were built separately. In the MS-AR model, it is necessary to pay attention to the assumptions of the data used, namely normal distribution and stationary. In the Prophet model, there are no special assumptions like those of the MS-AR model, but the Prophet model is good for data containing trends and seasonal patterns. The results of this study show that among the MS-AR models, the MS(2)-AR(3) model is the best model. In addition, the results show that the modified Prophet model performs better than the basic Prophet model. The goodness of model performance is measured by the Mean Absolute Percentage Error (MAPE) metric, with MAPE values for each model being 5.54% for MS(2)-AR(3), 3.38% for the Prophet base model, and 2.88% for Prophet modification. Based on the MAPE value, the Prophet (modified) model is able to predict the closing price of shares better than the MS(2)-AR(3) and Prophet (basic) models. The results of this study can be used by investors as a measuring tool in reading and determining stock price predictions.
Time-varying Distribution Analysis for Rainfall and Air Temperature Data in Jakarta in Response to Future Climate Change Setyawati, Suci Nur; Nurdiati, Sri; Mangku, I Wayan; Najib, Mohamad Khoirun
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 2 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i2.32780

Abstract

AbstractIndonesia is vulnerable to climate change (rainfall and air temperature), which can increase the chances of climatic disasters. An organized risk analysis is a strategic plan to minimize the impact. The purpose of this research is to estimate time-varying distribution parameters for normal, generalized extreme value (GEV), and lognormal distributions using fminsearch and MLE algorithms on rainfall and air temperature data in Jakarta, as well as visualize and analyze the best time-varying distribution. The maximum likelihood estimation (MLE) method is used for stationary distribution parameter estimation. The fminsearch algorithm is used for stationary and nonstationary distribution parameter estimation. The highest difference value of stationary distribution parameter results from both methods is 5.3768 mm for rainfall data and 0.2670°C for air temperature data. The results of the best distribution based on the AIC value are the 3-parameter lognormal distribution for rainfall data and the 4-parameter GEV distribution for air temperature data. Over time, the variance of rainfall increases, and the average air temperature increases with a fixed variance.
ANALISIS SUPPORT VECTOR REGRESSION DENGAN ALGORITMA GRID SEARCH UNTUK MEMPREDIKSI HARGA SAHAM Hermawan, Andri; Mangku, I Wayan; Ardana, N. K. Kutha; Sumarno, Hadi
MILANG Journal of Mathematics and Its Applications Vol. 18 No. 1 (2022): MILANG Journal of Mathematics and Its Applications
Publisher : School of Data Science, Mathematics and Informatics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/milang.18.1.41-60

Abstract

Pada artikel ini dikaji suatu metode yang dapat digunakan untuk meramalkan harga saham. Tujuan dari penelitian ini adalah memperkenalkan metode Support Vector Regression dengan Algoritma Grid Search untuk memprediksi harga saham INDF dan MYOR serta melakukan peramalan satu periode ke depan pada kedua perusahaan tersebut. Hasil kajian menghasilkan model prediksi terbaik untuk data saham INDF dengan nilai MAPE dan pada data testing berturut-turut sebesar 5.570% dan 79.9%, sedangkan untuk data saham MYOR diperoleh nilai MAPE dan pada data testing berturut-turut sebesar 2.954% dan 96%. Hasil penelitian juga menunjukkan prediksi harga saham INDF dan MYOR untuk satu periode selanjutnya (31 Desember 2021) berturut-turut sebesar Rp 6326.88/lembar dan Rp 2039.31/lembar.
KAJIAN PENDUGA FUNGSI RAGAM PROSES POISSON PERIODIK MAJEMUK DENGAN TREN FUNGSI PANGKAT Fajri, Ahmad; Mangku, I Wayan; Hadi Sumarno
MILANG Journal of Mathematics and Its Applications Vol. 18 No. 2 (2022): MILANG Journal of Mathematics and Its Applications
Publisher : School of Data Science, Mathematics and Informatics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/milang.18.2.87-97

Abstract

Pada artikel ini dibahas tentang pendugaan fungsi ragam pada proses Poisson periodik majemuk yang mempertimbangkan kehadiran tren fungsi pangkat. Penulisan artikel ini bertujuan untuk mengonstruksi penduga, memeriksa kekonsistenan penduga, menganalisis bias, ragam dan mean squared error (MSE) asimtotik penduga, serta menentukan ukuran interval pengamatan proses terpendek sehingga nilai dugaan yang diperoleh sudah mendekati parameter yang diduga menggunakan simulasi komputer. Hasil kajian yang telah diperoleh berupa rumusan penduga fungsi ragam, syarat-syarat agar penduga yang dirumuskan kokonsisten, rumusan bias asimtotik, ragam asimtotik dan MSE asimtotik penduga. Berdasarkan hasil simulasi diperoleh bahwa penduga sudah mendekati nilai parameter yang diduga jika panjang interval waktu pengamatan adalah 5500.
MODEL STOKASTIK EPIDEMIK SIRS INSIDEN TAK LINEAR DENGAN VAKSINASI Afriansyah, Dilla; Sumarno, Hadi; Mangku, I Wayan
MILANG Journal of Mathematics and Its Applications Vol. 19 No. 1 (2023): MILANG Journal of Mathematics and Its Applications
Publisher : School of Data Science, Mathematics and Informatics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/milang.19.1.11-22

Abstract

Matematika mempunyai peran penting dalam ilmu kesehatan salah satunya untuk membuat model penyebaran suatu penyakit. Salah satu penyakit yang dapat dibuat modelnya adalah penyakit difteri. Tujuan penelitian ini yakni memodifikasi model matematis difteri yang sudah ada menggunakan model stokastik continuous-time Markov chain (CTMC). Dalam penelitian ini pembahasan difokuskan pada peluang transisi, peluang wabah, dan bilangan reproduksi dasar. Bilangan reproduksi dasar mewakili jumlah rata-rata individu rentan menjadi terinfeksi karena masuknya satu inividu terinfeksi ke dalam subpopulasi rentan. Jika , maka hasil analisis memperlihatkan bahwa sistem populasi akan mengalami wabah penyakit, sedangkan jika , maka wabah penyakit tidak akan terjadi pada sistem populasi. Pada penelitian ini diperoleh model stokastik penyebaran penyakit difteri dengan dua fungsi yang berbeda yakni fungsi linear dan fungsi tak linear . Namun, keduanya memberikan hasil yang serupa yakni tidak akan terjadi wabah di dalam sistem ketika . Jika tingkat vaksinasi meningkat, maka bilangan reproduksi dasar menurun. Artinya semakin tinggi tingkat vaksinasi maka penyakit akan hilang di dalam sistem. Fungsi tak linear berpengaruh pada besarnya dan peluang wabah bergantung pada nilai konstanta α yang diberikan. Semakin besar nilai α, maka dan peluang wabah semakin kecil.
IMPLEMENTASI MODEL M/M/S PADA SISTEM ANTREAN PASIEN DI POLIKLINIK PRATAMA IPB DRAMAGA, KABUPATEN BOGOR, JAWA BARAT Imni, Salsabila Fitri; Sanjaya, Wardah; Chairunisa, Ghevira; Andriani, Rizka D; Henriyansah; Putri, Renda S. P.; Ekaputri, Dhea; Mangku, I Wayan
MILANG Journal of Mathematics and Its Applications Vol. 20 No. 1 (2024): MILANG Journal of Mathematics and Its Applications
Publisher : School of Data Science, Mathematics and Informatics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/milang.20.1.55-64

Abstract

Sistem antrean dapat ditemukan dalam kehidupan sehari-hari, baik di fasilitas publik seperti pelayanan bank dan pelayanan kesehatan, maupun di fasilitas swasta seperti tempat makan dan tempat belanja. Penelitian ini membahas mengenai penerapan model M/M/S pada sistem antrean pasien di Poliklinik Pratama IPB. Tujuan penelitian ini adalah untuk mengamati karakteristik sistem antrean yang diterapkan dan menentukan rata-rata laju kedatangan pasien, rata-rata laju pelayanan pasien, rata-rata banyaknya pasien di sistem, rata-rata panjang antrean, rata-rata lamanya pasien di sistem, dan rata-rata lamanya seorang pasien di antrean. Data penelitian diperoleh dari hasil observasi yang dilakukan selama tiga hari di Poliklinik Pratama IPB Dramaga, Kabupaten Bogor, Jawa Barat. Berdasarkan hasil pengamatan diperoleh bahwa sistem antrean yang diterapkan adalah M/M/2 dengan disiplin first come first served. Berdasarkan analisis data diperoleh beberapa hasil berikut. Rata-rata laju kedatangan pasien adalah 16.5 pasien/jam, rata-rata laju pelayanan pasien adalah 16.3 pasien/jam, rata-rata banyaknya pasien di sistem adalah 1.31, rata-rata panjang antrean adalah 0.988 orang, rata-rata lamanya pasien di sistem adalah 4.763 menit, dan rata-rata lamanya seorang pasien di antrean adalah 3.6 menit.
ANALISIS PERBANDINGAN KINERJA MODEL ARIMA DAN GEOMETRIC BROWNIAN MOTION UNTUK PREDIKSI HARGA SAHAM BBCA Nikmah Isnaeni Sakbaniyah; Rakhain Alyssa Humaira; M. Hadziq Rafli Fasya; Dave Ananda Osferi; Febby Dwi Kurniawati; I Wayan Mangku
MILANG Journal of Mathematics and Its Applications Vol. 21 No. 1 (2025): MILANG Journal of Mathematics and Its Applications
Publisher : School of Data Science, Mathematics and Informatics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/milang.21.1.21-34

Abstract

Saham merupakan salah satu jenis instrumen dalam pasar modal yang banyak diminati oleh investor karena memiliki potensi keuntungan yang menjanjikan. Meskipun begitu, investasi saham memiliki beberapa risiko seperti fluktuasi harga saham yang sulit diprediksi. Peramalan harga saham dapat menjadi salah satu upaya preventif yang dapat dilakukan sebelum berinvestasi. Penelitian ini menganalisis perbandingan kinerja model ARIMA (Autoregressive Moving Average) dan GBM (Geometric Brownian Motion) dalam memprediksi harga saham PT Bank Central Asia Tbk. Data historis saham yang digunakan dalam membangun model berada pada rentang waktu 10 Oktober 2023 - 10 Oktober 2024. Model ARIMA menggabungkan tiga komponen utama, yaitu Autoregressive, Integrated, dan Moving Average, sedangkan model GBM memanfaatkan konsep drift dan volatilitas untuk memodelkan pergerakan harga saham secara stokastik. Hasil penelitian menunjukkan bahwa model GBM memiliki nilai MAPE (Mean Absolute Percentage Error) 2.391%, sedangkan ARIMA memiliki nilai MAPE 3.431%. Berdasarkan nilai tersebut, diketahui bahwa model GBM memiliki nilai MAPE yang lebih kecil sehingga memberikan hasil peramalan yang lebih akurat dalam memprediksi harga saham BBCA. Penelitian memberikan wawasan penting bagi investor dalam memilih metode pemodelan yang tepat untuk mendukung pengambilan keputusan investasi.
Implementasi Penggunaan Generalisasi Thinning Process pada Penduga Fungsi Ragam Proses Poisson Periodik Majemuk Abdullah, Syarif; Mangku, I Wayan; Mursyidah, Himmatul; Huda, Mifathul; Ikhsan, Fajri; Chasanah, Sri Istiyarti Uswatun
Jambura Journal of Mathematics Vol 6, No 1: February 2024
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v6i1.22491

Abstract

This article implements the thinning process algorithm, which has been generalized for estimators of compound periodic Poisson processes. The use of generalizations in the algorithm has been prepared with a linear trend in the periodic elements. This research aims to discuss estimators of the variance function. The method used in this research is the simulation method. Simulation results using a generalized algorithm thinning process show that in the case of a limited observation time interval, some estimators are good enough to approach the actual value. As the value of n increases, the simulated value of the estimator moves towards the predicted value. This is following the lemmas, theorems, and consequences that have been discussed. It was also found that several estimators were quite slow. This results in the movement of the bias, variance, and MSE values of the estimators being slow, even though they are moving towards 0. So that further modifications can be made to the model being studied.
Co-Authors A.Tuti Rumiati Ade Irawan Ahmad Fajri Ahmad Fajri Aji Hamim Wigena Anang Kurnia Anas D Susila Andri Hermawan Andri Hermawan, Andri Andriani, Rizka D Anik Djuraidah Ardana, N. K. Kutha Arief Gusnanto ASEP SAEFUDDIN Atang Sutandi Auliya Fithry Bagus Sartono Bambang S Purwoko Bib Paruhum Silalahi Chairunisa, Ghevira Chasanah, Sri Istiyarti Uswatun Dave Ananda Osferi Deiby T Salaki Dewi Juliah Ratnaningsih Dhea Ekaputri Dilla Afriansyah Dillah Rismawati Ekaputri, Dhea Faisal Muhammad Faisal Muhammad, Faisal Fatimah Azzahra Febby Dwi Kurniawati Ghevira Chairunisa Hadi Sumarno Hadi Sumarno Henriyansah Henriyansah Herlina Hanum Herlina Hanum, Herlina Hermanto Siregar Himmatul Mursyidah Huda, Mifathul I Gusti Putu Purnaba Ikhsan Fajri, Ikhsan Imni, Salsabila Fitri Jajang Jajang Kusman Sadik Luthfi Izhar M. Hadziq Rafli Fasya Muhammad Wiranadi Utama N. K. Kutha Ardana Najib, Mohamad Khoirun Nikmah Isnaeni Sakbaniyah Nurul Indah Safitri Putri, Renda S. P. Rakhain Alyssa Humaira Renda S. P. Putri Retno Budiarti Rizka D Andriani Safitri, Nurul Indah Salsabila Fitri Imni Sanjaya, Wardah Setyawati, Suci Nur siswadi - Siti Muchlisoh Sri Nurdiati Syarif Abdullah Wardah Sanjaya Yulianty, Sherly