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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,

Author-ID : 314049

Agriculture, Biological Sciences & Forestry Computer Science & IT Control & Systems Engineering Earth & Planetary Sciences Energy Environmental Science Mathematics Public Health

Published : 31 Documents Claim Missing Document

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Articles

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The Application of Modeling Gamma-Pareto Distributed Data Using GLM Gamma in Estimation of Monthly Rainfall with TRMM Data Herlina Hanum; Aji Hamim Wigena; Anik Djuraidah; I Wayan Mangku
Sriwijaya Journal of Environment Vol 2, No 2 (2017): Water As A Vital Resource for Life
Publisher : Program Pascasarjana Universitas Sriwijaya

As a recently developed distribution, the application of Gamma-Pareto is limited to single variable modeling. A specific transformation of Gamma-Pareto (G-P) yields gamma distribution. Therefore, it is possible to use analysis based on gamma distribution (e.g. GLM) for modeling G-P distributed data. In this paper we study the application of modeling G-P distributed data using GLM gamma for monthly rainfall which observed in Sukadana Station. The modeling aims to analyze whether Tropical Rainfall Measuring Mission (TRMM) satellite data is a good estimator for unobserved station’s data. The transformed of station’s data were considered as response variable in GLM gamma. The explanatory variable is TRMM data in 9 grids around the station. There are two kinds of modeling i.e. model for whole data and extreme data. The results show that for both data the station’s data are G-P distributed and the transformed data are gamma distributed. TRMM rainfall data at each grid around the station can be used to estimate the observed data of monthly rainfall. The best model for both data contains dummy variables which correspond to inter quantile data. The coefficients of dummy variables in the best model may substitute the grouping or the correction in the previous studies.

Asymptotic Distribution of an Estimator for Variance Function of a Compound Periodic Poisson Process with Power Function Trend Muhammad Wiranadi Utama; I Wayan Mangku; Bib Paruhum Silalahi
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 6, No 4 (2022): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v6i4.10213

In this paper, an asymptotic distribution of the estimator for the variance function of a compound periodic Poisson process with power function trend is discussed. The periodic component of this intensity function is not assumed to have a certain parametric form, except it is a periodic function with known period. The slope of power function trend is assumed to be positive, but its value is unknown. The objectives of this research are to modify the existing variance function estimator and to determine its asymptotic distribution. This research begins by modifying the formulation of the variance function estimator. After the variance function is obtained, the research is continued by determining the asymptotic distribution of the variance function estimator of the compound periodic Poisson process with a power function trend. The first result is modification of existing estimator so that its asymptotic distribution can be determined. The main result is asymptotic normality of the estimator of variance function of a compound periodic Poisson process with power function trend.

A Study on the Estimator Distribution for the Expected Value of a Compound Periodic Poisson Process with Power Function Trend Nurul Indah Safitri; I Wayan Mangku; Hadi Sumarno
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

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

Confidence Intervals for the Mean Function of a Compound Cyclic Poisson Process in the Presence of Power Function Trend Faisal Muhammad; I Wayan Mangku; Bib Paruhum Silalahi
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 7, No 3 (2022): 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/ca.v7i3.15989

We consider the problem of estimating the mean function of a compound cyclic Poisson process in the presence of power function trend. The objectives of this paper are: (i) to construct confidence interval for the mean function of a compound cyclic Poisson process with significance level , (ii) to prove that the probability that the mean function contained in the confidence interval converges to , and (iii) to observe, using simulation study, that the probabilities of the mean function contained in the confidence intervals for bounded length of observation interval. The main results are a confidence interval for the mean function and a theorem about convergence of the probability that the mean function contained in confidence interval. The simulation study shows that the probability that the mean function contained in the confidence interval is in accordance with the theorem. The contribution of this study is to provide information for users regarding confidence interval for the mean function of a compound cyclic Poisson process in the presence of power function trend.

ANALISIS SUPPORT VECTOR REGRESSION DENGAN ALGORITMA GRID SEARCH UNTUK MEMPREDIKSI HARGA SAHAM Andri Hermawan; I Wayan Mangku; N. K. Kutha Ardana; Hadi Sumarno
MILANG Journal of Mathematics and Its Applications Vol. 18 No. 1 (2022): MILANG Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

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 Ahmad Fajri; I Wayan Mangku; Hadi Sumarno
MILANG Journal of Mathematics and Its Applications Vol. 18 No. 2 (2022): MILANG Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

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 Dilla Afriansyah; Hadi Sumarno; I Wayan Mangku
MILANG Journal of Mathematics and Its Applications Vol. 19 No. 1 (2023): MILANG Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

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

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.

Mixed Models of Non-Proportional Hazard and Application in The Open Distance Education Students Retention Data Dewi Juliah Ratnaningsih; Anang Kurnia; Asep Saefuddin; I Wayan Mangku
Journal of the Indonesian Mathematical Society VOLUME 28 NUMBER 3 (NOVEMBER 2022)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.28.3.1185.323-344

The problem that arises in the Cox model is that there are more than two types of covariates and the presence of random effects is a non-proportional hazard (NPH). One example of a case that involves many factors is student retention. Low student retention can lead to dropping out of college or failure in completing studies. The purpose of this study is to overcome the problem of NPH caused by the presenceof time-independent covariates, time-dependent covariates, and random effects. The research method uses simulation. Some of the modified models are the stratified Cox model, the extended Cox model, and the frailty model. The developed model is applied to distance education student retention data. The results of the study show that frailty and study programs provide considerable diversity in explaining thetotal diversity of the model. It can be concluded that frailty needs to be considered by UT to improve the quality of services to students. In addition, other covariates that have a significant effect on UT student learning retention modeling are age, domicile, gender, GPA, marital status, employment status, number of credits taken, and number of registered courses.

IMPLEMENTASI MODEL M/M/S PADA SISTEM ANTREAN PASIEN DI POLIKLINIK PRATAMA IPB DRAMAGA, KABUPATEN BOGOR, JAWA BARAT Salsabila Fitri Imni; Wardah Sanjaya; Ghevira Chairunisa; Rizka D Andriani; Henriyansah; Renda S. P. Putri; Dhea Ekaputri; I Wayan Mangku
MILANG Journal of Mathematics and Its Applications Vol. 20 No. 1 (2024): MILANG Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

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

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.

Confidence Intervals for the Mean Function of a Compound Cyclic Poisson Process in the Presence of Power Function Trend Muhammad, Faisal; Mangku, I Wayan; Silalahi, Bib Paruhum
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 7, No 3 (2022): 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/ca.v7i3.15989

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

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