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All Journal M A T H L I N E : Jurnal Matematika dan Pendidikan Matematika Indonesian Journal of Statistics and Its Applications
Mashuri Mashuri
Universitas Jenderal Soedirman, Indonesia
Computer Science & IT Education Mathematics Other

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Comparing of Car-Bym, Generalized Poisson, and Negative Binomial Models on Tuberculosis Data in Banyumas Districs: Pembandingan Model Car-Bym, Generalized Poisson, dan Binomial Negatif pada Data Tuberkolosis di Kabupaten Banyumas Jajang Jajang; Budi Pratikno; Mashuri Mashuri
Indonesian Journal of Statistics and Applications Vol 5 No 1 (2021)
Publisher : Statistics and Data Science Program Study, SSMI, IPB University, in collaboration with the Forum Pendidikan Tinggi Statistika Indonesia (FORSTAT) and the Ikatan Statistisi Indonesia (ISI)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/ijsa.v5i1p130-140

Abstract

In 2019 the number of people with TB (Tuberculosis) in Banyumas, Central Java, is high (1,910 people have been detected with TB). The number of people infected Tuberculosis (TB) in Banyumas is the count data and it is also the area data. In modeling, the parameter estimation and characteristic of the data need to be considered. Here, we studied comparing Generalized Poisson (GP), negative binomial (NB), and Poisson and CAR.BYM model for TB cases in Banyumas. Here, we use two methods for parameter estimation, maximum likelihood estimation (MLE) and Bayes. The MLE is used for GP and NB models, whereas Bayes is used for Poisson and CAR-BYM. The results showed that Poisson model detected overdispersion where deviance value is 67.38 for 22 degrees of freedom. Therefore, ratio of deviance to degrees of freedom is 3.06 (>1). This indicates that there was overdispersion. The folowing GP, NB, Poisson-Bayes and CAR-BYM are used to modeling TB data in Banyumas and we compare their RMSE. With refer to RMES criteria, we found that CAR-BYM is the best model for modeling TB in Banyumas because its RMSE is smallest.
Analysis Of Fractional Logistic Model Solution And Its Simulation On Human Development Index Data Of Cilacap District Agus Sugandha; Mashuri Mashuri; Danang Adi Pratama; Erni Supriyanti; Rima Anggraeni
Mathline : Jurnal Matematika dan Pendidikan Matematika Vol. 10 No. 3 (2025): Mathline : Jurnal Matematika dan Pendidikan Matematika
Publisher : Universitas Wiralodra

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31943/mathline.v10i3.931

Abstract

This research discusses the formation of the Fractional Logistic model and its solution analysis, as well as its simulation to predict the Human Development Index in Cilacap Regency using the Fractional Logistic growth model. This study uses secondary data obtained from the official website of the Central Statistics Agency of Cilacap Regency. Based on these data, the growth of the Human Development Index in Cilacap Regency has increased relatively. This shows the Cilacap community's good quality of life. Based on the environmental carrying capacity value of 73, a relative growth rate per year of 0.14273269 is obtained. This model predicts the Human Development Index in Cilacap Regency in 2024 and 2025. The prediction results for 2024 of 71.47 and 2025 of 71.67 are achieved when the fractional derivative order is one. The best approximate solution is obtained when the fractional derivative order is 1, 0.95 0.90, 0.85, 0.80 and 0.75.
Co-Authors Agus Sugandha Budi Pratikno Danang Adi Pratama Erni Supriyanti Jajang Jajang Rima Anggraeni