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All Journal JBIO: jurnal biosains (the journal of biosciences) CAUCHY: Jurnal Matematika Murni dan Aplikasi Althea Medical Journal Journal of the Indonesian Mathematical Society BAREKENG: Jurnal Ilmu Matematika dan Terapan JTAM (Jurnal Teori dan Aplikasi Matematika) Limits: Journal of Mathematics and Its Applications Journal of Epidemiology and Public Health Jambura Journal of Mathematics M A T H L I N E : Jurnal Matematika dan Pendidikan Matematika GREENOMIKA Jurnal Kesehatan Jurnal Pendidikan Administrasi Perkantoran (JPAP) Milang Journal of Mathematics and Its Applications Jurnal Indonesia Sosial Sains Proceeding Applied Business and Engineering Conference MILANG Journal of Mathematics and Its Applications
Retno Budiarti
Department Of Mathematics, Faculty Of Mathematics And Natural Sciences, Bogor Agricultural University, Jl. Meranti, Kampus IPB Darmaga, Bogor
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Confidence Interval for Variance Function of a Compound Periodic Poisson Process with a Power Function Trend Irawan, Ade; Mangku, I Wayan; Budiarti, Retno
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.v7i3.14836

Abstract

This research is a follow-up research of Utama (2022) on asymptotic distribution of an estimator for variance function of a compound periodic Poisson with the power function trend. The objectives of this research are (i) to formulate a confidence interval for the variance function of a compound periodic Poisson process with a power function trend and (ii) to prove the convergence to 1-α probability of the parameter included in the confidence interval. This research process begins with a review of the existing formulation of the variance function estimator and its asymptotic distribution. Next, the confidence interval for the variance function of the compound periodic Poisson process with a power function trend is formulated and the convergence to 1-α is determined. After obtaining the confidence interval, the research continued by conducting computer simulations to confirmed the results obtained analytically. The results obtained show that the confidence interval for the variance function of a compound periodic Poisson process with a power function trend converges to 1-α both analytically and numerically for different finite time intervals.
Modelling Dependencies of Stock Indices During Covid-19 Pandemic by Extreme-Value Copula Budiarti, Retno; Intansari, Kumala; Purnaba, I Gusti Putu; Septyanto, Fendy
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.v7i3.15109

Abstract

Quantifying dependence among variables is the core of all modelling efforts in financial models. In the recent years, copula was introduced to model the dependence structure among financial assets return, and its application developed fast. A large number of studies on copula have been performed, but the study of multivariate extremes related with copulas was quite behind in comparison with the research on copulas. The COVID-19 pandemic is an extreme event that has caused the collapse of various economic activities which resulted in the decline of stock prices. The modelling of extreme events is therefore important to mitigate huge financial losses. Extreme-value copula can be suitable to quantify dependencies among assets under an extreme event. In this paper, we study the modelling of extreme value dependence using extreme value copulas on finance data. This model was applied in the portfolio of the IDX Composite Index (IHSG), Straits Times Index (STI) and Kuala Lumpur Stock Exchange (KLSE). Each individual asset return is modelled by the ARMA-GARCH and the joint distribution is modelled using extreme value copulas. This empirical study showed that Gumbel copula is the most appropriate extreme value copulas for the three indices. The results of this study are expected to be used as a basis for investors in the formation of a portfolio consisting of 2 financial assets and a portfolio consisting of 3 financial assets. 
Exploring Diabetes Mellitus' Impact on Tuberculosis Outcomes: A Comprehensive Comparative Study Diana, Adawiyah Putri; Adiwinoto, Ronald Pratama; Budiarti, Retno; Soedarsono; Prasetya, Hanung; Putra, Oki Nugraha
Journal of Epidemiology and Public Health Vol. 10 No. 2 (2025)
Publisher : Masters Program in Public Health, Universitas Sebelas Maret, Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26911/jepublichealth.2025.10.02.03

Abstract

Background: Tuberculosis (TB) remains among the top ten global causes of mortality, with approximately 1.3 million deaths annually. Diabetes elevates the risk of active TB and treatment failure, potentially increasing drug-resistant TB (DR-TB). This study aimed to compare treatment success rates between TB patients with and without diabetes mellitus (DM) at Dr. Ramelan Central Naval Hospital, Surabaya.Subjects and Method: This cross-sectional study was conducted from January 2019 to December 2023 at Dr. Ramelan Central Naval Hospital Surabaya. A total of 158 patients with TB-DM and TB-NonDM were selected using total sampling. The independent variables were the Presence of Diabetes Mellitus in TB patients (TB-DM vs. Non-TB-DM). The dependent variable was the treatment success rate. The data were collected from patient medical records and analyzed using a chi-square test to compare treatment outcomes between TB-DM and TB-Non-DM patients.Results: The analysis included 158 medical records. Predominantly affecting those over 45 years, both TB-DM and TB-Non-DM patients commonly underwent six months of treatment, with success rates of 78% in TB-DM and 82.4% in TB-Non-DM cases. The chi-square test yielded a p-value of 0.511, indicating no significant difference in treatment success between the groups. However, older age and HIV-positive status were associated with lower odds of treatment success.Conclusion: Success rates were similar between the groups, showing no significant difference based on DM status. Despite similar success rates, older age and HIV-positive status were associated with lower odds of treatment success.
Comparative Analysis of Machine Learning Algorithms on Family Wellness Classification Budiarti, Retno; Hemarani, Febri; Reza, Mohammad; Mulyasari, Rindi Melati
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 9, No 2 (2024): 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.v9i2.28259

Abstract

Family welfare is a state in which a family can experience happiness, have a decent quality of life, and be sufficient in meeting primary and secondary needs in family life. One factor that influences family welfare is the amount of per capita expenditure. This study aims to compare the performance of three machine learning algorithms, namely KNN (K-Nearest Neighbors), random forest, and naive Bayes, in classifying the status of families per province in Indonesia as prosperous or not prosperous. The data used in this study is demographic and social statistics data from the years 2017-2021, obtained from the bps.go.id website. The first statistical analysis conducted is principal component analysis (PCA) with 9 predictor variables. PCA produces four principal components which are then used in the KNN, random forest, and naive Bayes methods. The analysis results from the KNN, random forest, and naive Bayes methods each yield an F1-score of 65.46%, 68%, and 69.44%, respectively.
Determining Tomato Crop Agricultural Insurance Premium for COVID-19 Pandemic Setyawan, Binar Aulia; Purnaba, I Gusti Putu; Budiarti, Retno
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 8, No 2 (2023): 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.v8i2.22782

Abstract

One type of insurance known as parametric insurance has an agreement for predetermined events made at the beginning of the contract between the insurer (insurance firm) and the insured (farmer). When the causative event occurs, the provision applies that insurer must pay insured with some amount of money (damage compensation). Ozaki has formulated parametric method of premium rates for agricultural insurance build upon yields in specific area. Indonesian Ministry of Agriculture uses this method to ensure that farmers can re-plant crops in following planting season if a crop failure occurs. However, the COVID-19 pandemic's losses were not covered by this method. Given this, we would like to develop agricultural insurance models for tomato crops which figure out COVID-19 pandemic. For make it easier to see the price of tomato commodity due to impact of COVID-19 pandemic, in this research we will take a case study on agriculture managed by PT Mitra Tani Parahyangan. This company is engaged in the horeca business, so it has been greatly affected by the quarantine policy. The results of this study are suggestions for policy makers in anticipation if a pandemic occurs again, it help farmers and Indonesia’s food availability will be maintained.
Bias Correction of Lake Toba Rainfall Data Using Quantile Delta Mapping Rafhida, Syukri Arif; Nurdiati, Sri; Budiarti, Retno; Najib, Mohamad Khoirun
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 9, No 2 (2024): 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.v9i2.29124

Abstract

Lake Toba, located in North Sumatra, is the largest tectonic and volcanic lake in Indonesia. Lake Toba has an equatorial climate characterized by abundant rainfall throughout the year. High rainfall, coupled with annual increases due to climate change, results in a vulnerability to the unpredictable extreme weather, causing harm to the surrounding communities. Consequently, a rainfall prediction model is needed to anticipate the impacts of such extreme rainfall. One of the rainfall prediction models used is ERA5-Land. However, this prediction model has biases that can be avoided. A method that can be used is the statistical bias correction using the quantile delta mappings (QDM) by correcting ERA5-Land model data against BMKG observation data. The QDM method used in this study employs two types of methods: monthly and full distribution. The results shows that both methods can improve biases at Silaen, Laguboti, and Doloksanggul stations, as well as improve the model during the equatorial dry seasons in May, June, July, and August. However, the first method improves the model distribution more in Silaen and Laguboti, while the second method improves the model distribution more in Doloksanggul.
Parametric Survival Model on IPB University’s Graduation Data Nashiruddin, Muhammad Abdurrasyid; Sumarno, Hadi; Budiarti, Retno
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 2 (2023): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i2.12681

Abstract

Graduation is one of the assessment criteria in the college accreditation process. Students who graduate on time will assist in the assessment of college accreditation. This study aims to determine the distribution that best fits student graduation data and determine the best model to analyze the factors that determine student graduation from IPB University. This study presents some parametric models in survival analysis, specifically, the accelerated failure time (AFT) model and the proportional hazard (PH) model. The objective of this research is to compare the performance of PH model and the AFT models in analyzing the significant factors affecting the student graduation at the IPB University. Based on the study's results, the distribution according to student graduation data is the Burr XII distribution, and the best model using the AIC criteria is the PH Burr XII model. The factors that influence the graduation of IPB University students are gender, faculty, GPA, regional origin, and school status. 
Effects of grey mangrove leaf extract (Avicennia marina) on the growth of Staphylococcus aureus Priambodo, Bima; Budiarti, Retno; Rahadianto, Rahadianto; Nefertiti, Eva
JURNAL BIOSAINS Vol. 10 No. 2 (2024): JBIO : JURNAL BIOSAINS (THE JOURNAL OF BIOSCIENCES)
Publisher : Universitas Negeri Medan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24114/jbio.v10i2.43222

Abstract

The emergence and spread of methicillin-resistant Staphylococcus aureus in recent decades complicates the antibiotic therapy. The grey mangrove (Avicennia marina) has flavonoid, terpenoid, saponin, phenolic, tannin, and alkaloid chemical compounds that have antimicrobial activity, thus potentially inhibiting Staphylococcus aureus. This study aims to examine the effects of the grey mangrove (Avicennia marina) leaf extracts on the growth of Staphylococcus aureus. This research uses laboratory experimental design with disc diffusion method to test the inhibition of Staphylococcus aureus bacteria growth in Mueller-Hinton medium. There were 6 treatment groups, namely negative control of 0.2% DMSO,  positive control of amoxicillin 30 µg, Avicennia marina leaf extract at concentration of 25%, 50%, 75%, and 100%. The results of this research showed that Avicennia marina leaf extract produces inhibition zone of 7.06 mm, 8.51 mm, 10.07 mm, 13.29 mm at concentration of 25%, 50%, 75%, and 100%. Meanwhile, positive control produces inhibiton zone of 23.65 mm, and negative control has no inhibition zone. The statistical tests using one-way ANOVA resulted in a significance value of less than 0.05 (p<α). The conclusion of this study showed that the grey mangrove (Avicennia marina) leaf extract at 100% concentration is the most effective treatment group in inhibiting the growth of Staphylococcus aureus, although the inhibition was not much better when compared to the inhibition of the positive control group.
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 Ade Irawan Adriani, Ika Reskiana Aldinasyah, Monicha Zalzabilla Anang Kistyanto Andre Dwijanto Witjaksono Asri Rahmawati Berlian Setiawaty Bib Paruhum Silalahi Chalimatusadiah Chalimatusadiah D. S. Rahmawati Daniel Happy Putra Dara Irsalina Dewi, Komang Nonik Afsari Diana, Adawiyah Putri Donny Citra Lesmana Dwi Fidiana Endar Hasafah Nugrahani Erliana, Windiani Fendy Septyanto Garianto, Efyluk Grifin Ryandi Egeten Hadi Sumarno Helynda Mulya Arga Retha Helynda Mulya Arga Retha Hemarani, Febri Herdiyantini, Mita I Gusti Putu Purnaba I Wayan Mangku Intansari, Kumala Khairiati, Alfi Khan, Joan Manjaruni, Vivin Aprilia Mohammad Reza Muhammad Yusuf Sulaiman Mulyasari, Rindi Melati Najib, Mohamad Khoirun Nashiruddin, Muhammad Abdurrasyid Nefertiti, Eva Nur Agustiani Parwati, Lusiana Sani Prasetya, Hanung Priambodo, Bima Putra, Hilman Yusupi Dwi Putra, Oki Nugraha Rafhida, Syukri Arif Rahadianto, Rahadianto Rahmah, Salsabilla Rahmawati, D. S. Rizki, Kurniadi Ronald Pratama Adiwinoto Ruhiyat Ruhiyat S. Soedarsono Setyawan, Binar Aulia Silalahi, Romaito Br siswadi - Sitepu, Sanfriska Br Sri Nurdiati Sudiarta, Ketut Edy Sulaiman, Muhammad Yusuf Titut Harnanik Utami, Nadila Rizqi Windiani Erliana Yulianty, Sherly