Article Per Year (5 Year)
p-Index From 2019 - 2024
0.817
P-Index
This Author published in this journals
All Journal Desimal: Jurnal Matematika M A T H L I N E : Jurnal Matematika dan Pendidikan Matematika InPrime: Indonesian Journal Of Pure And Applied Mathematics
Mahmudi Mahmudi
UIN Syarif Hidayatullah Jakarta
Computer Science & IT Education Mathematics Social Sciences

Published : 4 Documents Claim Missing Document
Claim Missing Document
Check
Articles

Found 4 Documents
Search

 1 
Fit of the 2011 Indonesian Mortality Table to Gompertz's and Makeham's Law using Maximum Likelihood Estimation Dino Agustin Putra; Nina Fitriyati; Mahmudi Mahmudi
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 1, No 2 (2019)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (2531.889 KB) | DOI: 10.15408/inprime.v1i2.13276

Abstract

AbstractThis research discusses the estimation of the parameters for Gompertz’s law and Makeham’s law using the Maximum Likelihood Estimation method. A numerical approach to estimate the parameters of Gompertz’s law is the Newton-Raphson method. In the Makeham’s law, we use the Lagrange multiplier method to solve constraints of 0.001<A<0.003, 10^(-6)<B<10^3 and 1.075<C<1.115, and Broyden as a method to estimate the parameter numerically. The estimation result shows that parameter B converges to 0.005749 and parameter C converges to 1.024738 in the Gompertz’s law. In the Makeham’s law, the estimated parameters that satisfied the constraints are A converges to 0.00300344,  B converges to 0.0002716465, and C converges to 1.113395. Based on the Average Relative Error (ARE) that calculated from the estimated for px, the 2011 Indonesian Mortality Table (the 2011 TMI) for men and for women are more accurate when approached using the Gompertz’s law than the Makeham’s law. The estimated for px uses the Gompertz’s law are very close to the px at the 2011 TMI (with Absolute Percentage Errors of less than 1%) at age intervals, for men: 0 – 10 years, 10 – 20 years, 20 – 30 years, and 60 – 70 years, and for women: 0 – 10 years, 10 – 20 years, and 70 – 80 years.Keywords: parameter estimation; Newton-Raphson method; Broyden method; Lagrange Multiplier method. AbstrakPenelitian ini membahas mengenai estimasi parameter hukum mortalitas Gompertz’s dan hukum mortalitas Makeham’s menggunakan metode Maximum Likelihood Estimation. Pendekatan numerik untuk estimasi parameter hukum mortalitas Gompertz dilakukan menggunakan metode Newton-Raphson. Untuk mengatasi syarat batas 0.001<A<0.003, 10^(-6)<B<10^3 dan 1.075<C<1.115, pada estimasi parameter hukum mortalita Makeham digunakan metode pengali Lagrange dan pendekatan numerik metode Broyden. Hasil estimasi menunjukkan bahwa parameter B konvergen ke 0,005749 dan parameter C konvergen ke 1,024738 pada hukum mortalitas Gompertz. Pada hukum mortalitas Makeham’s, hasil estimasi parameter yang memenuhi syarat batas adalah nilai A konvergen ke 0,00300344, B konvergen ke 0,0002716465, dan C konvergen ke 1,113395. Berdasarkan nilai Average Relative Error (ARE) yang dihitung untuk estimasi , Tabel Mortalita Indonesia (TMI 2011) untuk pria dan untuk wanita lebih sesuai jika didekati menggunakan hukum Gompertz daripada hukum Makeham. Estimasi  menggunakan pendekatan hukum Gompertz berada sangat dekat dengan nilai  pada TMI 2011 (dengan Mean Absolute Percentage Error kurang dari 1%) pada interval usia, untuk pria: 0 – 10 tahun, 10 – 20 tahun, 20 – 30 tahun, dan 60 – 70 tahun, dan untuk wanita: 0 – 10 tahun, 10 – 20 tahun, dan 70 – 80 tahun.Kata kunci: estimasi parameter; metode Newton-Raphson; metode Broyden; metode Pengali Lagrange.
Forecasting Indonesian inflation using a hybrid ARIMA-ANFIS Nina Fitriyati; Mahmudi Mahmudi; Madona Yunita Wijaya; Maysun Maysun
Desimal: Jurnal Matematika Vol 5, No 3 (2022): Desimal: Jurnal Matematika
Publisher : Universitas Islam Negeri Raden Intan Lampung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24042/djm.v5i3.14093

Abstract

This paper discusses the prediction of the inflation rate in Indonesia. The data used in this research is assumed to have both linear and non-linear components. The ARIMA model is selected to accommodate the linear component, while the ANFIS method accounts for the non-linear component in the inflation data. Thus, the model is known as the hybrid ARIMA-ANFIS model. The clustering method is performed in the ANFIS model using Fuzzy C-Mean (FMS) with a Gaussian membership function. Consider 2 to 6 clusters. The optimal number of clusters is assessed according to the minimum value of the error prediction. To evaluate the performance of the fitted hybrid ARIMA-ANFIS model, it can be compared to the classical ARIMA model and with the ordinary ANFIS model. The result reveals that the best ARIMA model for inflation prediction in Indonesia is ARIMA(2,1,0). In the hybrid ARIMA(2,1,0)-ANFIS model, two clusters are optimal. Meanwhile, the optimum number of clusters in the ordinary ANFIS model is six. The comparison of prediction accuracy confirms that the hybrid model is superior to the individual model alone of either ARIMA or ANFIS model.
On Super (a,d)-C_3- Antimagic Total Labeling of Dutch Windmill Graph D_3^m Yanne Irene; Mahmudi Mahmudi; Nurmaleni Nurmaleni
Mathline : Jurnal Matematika dan Pendidikan Matematika Vol. 9 No. 1 (2024): Mathline: Jurnal Matematika dan Pendidikan Matematika
Publisher : Universitas Wiralodra

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31943/mathline.v9i1.565

Abstract

This paper  is aimed to investigate the existence of super (a,d)-C_3- antimagic total labeling of dutch windmill graph D_3^m . The methods to achieves the goal was  taken in three step. First of all determine the edge and vertices notation on dutch windmill graph . At the second step, labeling the vertices and edges of several dutch windmill graphs, then obtained the pattern. Finally pattern must be proven to become theorem. Based on the study, The Dutch Windmill Graph D_3^m, with m>=2 has super  (14m+9,5)-C_3- antimagic total labeling, super (13m+8,3)-C_3-  antimagic total labeling, super (12m+9.,5)-C_3-  antimagic total labeling, super (11m+10.,7)-C_3-  antimagic total labeling, super (10m+8.,3)-C_3-  antimagic total labeling.
The Effect of Ensemble Averaging Method on Rainfall Forecasting in Jakarta Using ARIMA and ARIMAX Mahmudi Mahmudi; Afnenda Rachmalia Hidayat; Madona Yunita Wijaya
Mathline : Jurnal Matematika dan Pendidikan Matematika Vol. 9 No. 2 (2024): Mathline: Jurnal Matematika dan Pendidikan Matematika
Publisher : Universitas Wiralodra

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31943/mathline.v9i2.608

Abstract

This research discusses rainfall modeling using ARIMA and ARIMAX models in Jakarta. This is important because rainfall forecasting in Jakarta has a significant impact on flooding and infrastructure. The focus of this research is on significant ARIMA and ARIMAX models, which are then subtotaled using ensemble averaging. Humidity and temperature variables are of particular interest in ARIMAX modeling due to their high correlation with rainfall. This quantitative research uses secondary data analysis from Tanjung Priok and Kemayoran Stations through the BMKG website, from July 2018 to June 2023. The results obtained at Tanjung Priok Station there are five significant ARIMA models and three significant ARIMAX models. While at Kemayoran Station there are 6 significant ARIMA models and two significant ARIMAX models. After using the ensemble averaging method on both ARIMA and ARIMAX models, the resulting SMAPE value is not better than the best ARIMA or ARIMAX models at both stations. Of all the models performed, the best model in forecasting with the smallest SMAPE is ARIMAX (0,0,1) at Tanjung Priok Station which is 37.83% and at Kemayoran Station which is 27.59%. This research provides new insights and significant contributions in understanding and developing rainfall forecasting in Jakarta using the ensemble averaging method.
Co-Authors Afnenda Rachmalia Hidayat Dino Agustin Putra Irene, Yanne Maysun Maysun Nina Fitriyati Nurmaleni Nurmaleni Wijaya, Madona Yunita