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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 BAREKENG: Jurnal Ilmu Matematika dan Terapan 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 Economics, Econometrics & Finance Energy Engineering Environmental Science Mathematics Mechanical Engineering Physics Public Health Transportation

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Asymptotic Distribution of an Estimator for Variance Function of a Compound Periodic Poisson Process with Power Function Trend Utama, Muhammad Wiranadi; Mangku, I Wayan; Silalahi, Bib Paruhum
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

Abstract

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.
ASYMPTOTIC DISTRIBUTIONS OF ESTIMATORS FOR THE MEAN AND THE VARIANCE OF A COMPOUND CYCLIC POISSON PROCESS Adriani, Ika Reskiana; Mangku, I Wayan; Budiarti, Retno
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 1 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss1pp0453-0464

Abstract

A stochastic process has an important role in modeling various real phenomena. One special form of the stochastic process is a compound Poisson process. A compound Poisson process model can be extended by generalizing the corresponding Poisson process. One of them is using a cyclic Poisson process. Our goals in this research are to determine the asymptotic distribution of the estimator for the mean and the variance of this process. In this paper, the problems of estimating the mean function and the variance function of a compound cyclic Poisson process are considered. We do not assume any parametric form for the intensity function except that it is periodic. We also consider the case when only a single realization of the cyclic Poisson process is observed in a bounded interval. Consistent estimators for the mean and variance functions of this process have been proposed in respectively. This paper introduces a set of novel theorems that, to the best of our knowledge, are not available in the existing literature and contribute original results to the field. Asymptotic distributions of these estimators are established when the size of the observation interval indefinitely expands. Asymptotic distributions of and are, respectively and as .
Co-Authors A.Tuti Rumiati Adriani, Ika Reskiana 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 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 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 Rismawati, Dillah Rizka D Andriani Safitri, Nurul Indah Salsabila Fitri Imni Sanjaya, Wardah Setyawati, Suci Nur siswadi - Siti Muchlisoh Sri Nurdiati Syarif Abdullah Utama, Muhammad Wiranadi Wardah Sanjaya Yulianty, Sherly