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All Journal Basis : Jurnal Ilmiah Matematika Al-Aqlu : Jurnal Matematika, Teknik dan Sains Diophantine Journal of Mathematics and Its Applications
Kurniawan, Andro
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Agriculture, Biological Sciences & Forestry Biochemistry, Genetics & Molecular Biology Computer Science & IT Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Engineering Industrial & Manufacturing Engineering Mathematics

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Comparison of Robust Regression Methods: Least Trimmed Squares and Maximum Likelihood for Handling Outliers Kurniawan, Andro; Oktarina, Cinta Rizki; Sabarinsyah, Sabarinsyah
Diophantine Journal of Mathematics and Its Applications Vol. 4 No. 2 (2025): Vol. 4 No. 2 (2025)
Publisher : UNIB Press

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.33369/diophantine.v4i2.46149

Abstract

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.
ANALISIS INTEGRAL FRAKSIONAL FUNGSI HIPERBOLIK: KASUS TANGEN DAN COTANGEN: Fractional Integral Analysis of Hyperbolic Function: The Case of Tangent and Cotangent Janan, Syifaul; Kurniawan, Andro
Al-Aqlu: Jurnal Matematika, Teknik dan Sains Vol. 4 No. 1 (2026): Januari 2026
Publisher : Yayasan Al-Amin Qalbu

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.59896/aqlu.v4i1.539

Abstract

This study examines the Riemann-Liouville fractional integral for hyperbolic tangent and cotangent functions with order  using Maclaurin series division method and power function fractional integral theorem. Results show the fractional integral of hyperbolic tangent is expressed as a fractional power series with gamma function coefficients, while hyperbolic cotangent has a singular term . MATLAB visualization shows α variations produce different growth characteristics. Hyperbolic tangent is regular with odd function symmetry, while hyperbolic cotangent is singular around the origin. This research provides explicit formulas for fractional calculus applications
Representasi Integral Fraksional Fungsi Secan Hiperbolik dan Cosecan Hiperbolik Janan, Syifaul; Harlianto, Didi; Kurniawan, Andro
Basis : Jurnal Ilmiah Matematika Vol. 5 No. 1 (2026): BASIS: Jurnal Ilmiah Matematika
Publisher : Universitas Mulawarman

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30872/jhq2s746

Abstract

Penelitian ini mengkaji representasi integral fraksional Riemann–Liouville pada fungsi secan hiperbolik dan cosecan hiperbolik menggunakan pendekatan deret Maclaurin. Kebaruan penelitian ini terletak pada perolehan bentuk eksplisit integral fraksional kedua fungsi tersebut serta analisis peran singularitas terhadap validitas representasi analitis. Hasil analisis menunjukkan bahwa fungsi secan hiperbolik dapat direpresentasikan secara analitis melalui deret pangkat yang konvergen pada domain |t| < π/2 sehingga integral fraksionalnya konsisten dengan integral klasik. Sebaliknya, fungsi cosecan hiperbolik memiliki singularitas di titik asal yang membatasi representasi analitisnya hanya pada suku non-singular. Implikasi matematis dari hasil ini menunjukkan adanya keterbatasan pendekatan deret untuk fungsi bersingular. Simulasi numerik menggunakan Matlab mendukung hasil teoritis dan memperlihatkan kesesuaian perilaku integral fraksional pada kedua fungsi tersebut.
Co-Authors Cinta Rizki Oktarina Harlianto, Didi Sabarinsyah, Sabarinsyah Syifaul Janan