Diophantine Journal of Mathematics and Its Applications

Comparison of Robust Regression Methods: Least Trimmed Squares and Maximum Likelihood for Handling Outliers

2025-12-11T04:35:55+00:00

This study investigates the determinants of per capita expenditure in 154 regencies and cities across Sumatra Island. The use of the Ordinary Least Squares method is deemed inappropriate due to violations of classical assumptions and the presence of outliers within the dataset. To address these issues, robust regression approaches are applied, specifically M-estimation and Least Trimmed Squares (LTS). The dependent variable in the analysis is per capita expenditure, while the explanatory variables include poverty line, human development index, average years of schooling, and expected years of schooling. The estimation procedures are performed using both raw and standardized data. The empirical results demonstrate that each independent variable significantly influences per capita expenditure under both robust estimation techniques. To determine the most reliable method, the residual standard error is used as the evaluation criterion. The outcomes indicate that the LTS estimator applied to standardized data provides the lowest error value, suggesting that it is the most suitable approach for estimating the regression parameters associated with per capita expenditure in Sumatra.

Pananganan Data Hilang pada Data Bangkitan Bivariate Gamma

2025-12-11T05:36:50+00:00

Missing data is a problem in data processing that can reduce the quality of analysis results if not addressed. This study aims to evaluate the performance of two imputation methods, namely Random Forest Imputation (RF) and Classification and Regression Tree (CART), at various levels of missing value proportions, namely 5%, 10%, 15%, and 20%. The data used in this study are Bivariate Gamma data of 200 observations with two variables, which were generated using RStudio software. The evaluation was carried out based on the correlation value between the imputed data and the original data, as well as the error measures Mean Absolute Percentage Error (MAPE) and Root Mean Square Error (RMSE). The results showed that at the missing value levels of 5% and 10%, the CART method produced the smallest MAPE and RMSE values, so that the CART method was the best method, although there was no significant difference between the RF method and the 10% missing value data. At 15% and 20% missing values, the RF method demonstrated superior performance with smaller MAPE and RMSE values compared to CART. Overall, the CART method is more suitable for use with a low proportion of missing values, while the RF method provides more stable performance at a high proportion of missing values. The results of this study provide recommendations for selecting a more appropriate imputation method based on the level of missing data.

Penerapan Metode Logika Fuzzy Sugeno dalam Pengambilan Keputusan Penentuan Jumlah Produksi

2025-06-25T05:17:44+00:00

The rapid development of the industry has led to increasingly fierce competition among companies, driving the need for operational efficiency and maximum profit. One of the main challenges faced by companies is determining the optimal production quantity to meet market demand and manage inventory efficiently. Inaccuracies in production planning, such as excess or insufficient stock, can reduce cost efficiency and customer satisfaction. The production decision-making process is often faced with uncertainty caused by limited information and incomplete data, making traditional approaches such as statistical calculations not always effective. As a solution, the Fuzzy logic method, particularly the Sugeno method, offers a flexible approach to managing uncertainty. This method uses human logic-based rules to model the relationship between demand, inventory, and production quantity adaptively. This research aims to explore the application of the Fuzzy Sugeno method in determining the optimal production quantity based on demand and supply data. Based on the analysis of tests conducted on the production quantity calculation application using the Fuzzy Sugeno method, a truth value of 81.63% was obtained. This high truth level indicates that the implementation of the Fuzzy Sugeno method is effective in determining the production quantity.

Pengoptimalan Portofolio Saham dengan Capital Asset Pricing Model dan Algoritma Simulated Annealing

2025-12-02T09:06:07+00:00

Stock investment has become increasingly popular in Indonesia, and the construction of an optimal portfolio is essential for effective risk and return management. This study integrates the Capital Asset Pricing Model (CAPM) with the Simulated Annealing algorithm to optimize stock portfolios. The Simulated Annealing algorithm enables flexible and realistic portfolio management by addressing non-linear complexities and market constraints. In addition, this study develops a Graphical User Interface (GUI)-based application using Python to assist investors in calculating and determining optimal portfolio allocations. The application utilizes stock data and investment parameters as inputs and produces optimal allocation outputs based on CAPM and heuristic solutions generated by the Simulated Annealing algorithm. This research offers an efficient and adaptive solution for portfolio optimization in a fluctuating market environment.

Probability Generating Functions: Theory and Applications to Distribution Generation, Branching Processes and Queueing Model

2026-01-29T10:41:13+00:00

The probability generating function (PGF) of a discrete random variable is a concise way to describe the corresponding probability distribution and facilitate analysis. This paper will revisit and explore certain key properties of the PGFs, focusing on structural properties, moment characterization and stability under convolution. Through applications to distribution generation, branching processes, and queueing models, PGFs are shown to provide clear insight into extinction probabilities and steady-state behavior. The results confirm that probability generating functions provide a coherent and useful framework for both theory and applications in discrete stochastic modelling.