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All Journal Journal of Science and Applicative Technology Unisda Journal of Mathematics and Computer Science (UJMC) Delta: Jurnal Ilmiah Pendidikan Matematika Variance : Journal of Statistics and Its Applications Jurnal Statistika dan Matematika (Statmat) Mathematics and Applications (MAp) Journal RENATA Jurnal Pengabdian Masyarakat Kita Semua Amalgamasi: Journal of Mathematics and Applications
Andi Fitriawati
Institut Teknologi Sumatera
Humanities Civil Engineering, Building, Construction & Architecture Computer Science & IT Decision Sciences, Operations Research & Management Earth & Planetary Sciences Economics, Econometrics & Finance Education Electrical & Electronics Engineering Energy Engineering Materials Science & Nanotechnology Mathematics Mechanical Engineering Physics Other

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Journal : Variance : Journal of Statistics and Its Applications

 1 
PEMODELAN KEBERGANTUNGAN DALAM MENGKONSTRUKSI DISTRIBUSI BIVARIAT COPULA FRANK PADA DATA MARGINAL DISKRIT MELALUI TRANSFORMASI NORMAL STANDAR DAN JITTERS Andi - Fitriawati; Dani Al Mahkya; Radot MH Siahaan; Dian Anggraini
VARIANCE: Journal of Statistics and Its Applications Vol 2 No 1 (2020): VARIANCE: Journal of Statistics and Its Applications
Publisher : Statistics Study Programme, Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Pattimura

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/variancevol2iss1page1-13

Abstract

Data diskrit merupakan data empirik hasil realisasi variabel acak diskrit maupun kontinu. Ketika memiliki dua jenis data diskrit, seringkali ingin dikonstruksi distibusi bivariatnya untuk berbagai keperluan, baik fungsi peluang maupun fungsi distribusinya. Namun, saat data yang dimiliki terdapat kebergantungan, maka mengkonstruksi distibusi bivariatnya tidaklah mudah. Oleh sebab itu, digunakan Copula. Permasalahan lain timbul ketika data yang dimiliki tidak hanya memiliki kebergantungan tetapi juga berasal dari marginal diskrit. Berdasarkan teorema Sklar, penggunaan Copula dalam mengkonstruksi distribusi bivariat pada marginal diskrit akan menghasilkan suatu Copula C yang tidak unik. Akibatnya akan menimbulkan interprestasi yang tidak jelas, terutama untuk sifat kebergantungannya. Oleh sebab itu, diperlukan suatu teknik untuk mengkonstruksi distribusi bivariat dari data tersebut, yaitu dengan mengkontinukan distribusi marginalnya. Mengkontinukan distribusi marginalnya dilakukan melalui transformasi normal standar dan jitters. Hasil trasnformasi mampu mempresentasikan data aslinya. Hal ini terlihat dari perilaku penyebaran data dan ukuran kebergantungan dari data hasil transformasi dengan data aslinya adalah sama. Ukuran kebergantungan yang digunakan, yaitu Korelasi Pearson dan Kendall’s tau. Selanjutnya, hasil transformasi ini kemudian digunakan untuk mengkontrusksi distribusi bivariat dari data yang dimiliki menggunakan Copula. Copula yang digunakan adalah Copula Frank dengan asumsi bahwa data tidak memiliki kebergantungan ekor atas maupun bawah. Jadi, fungsi peluang bivariat dan/atau fungsi distribusi bivariat dari data hasil transformasi mempresentasikan fungsi peluang bivariat dan/atau fungsi distribusi bivariat dari data aslinya. Seluruh prosesnya akan diilustrasikan melalui data simulasi.
ANALYSIS OF THE EFFECTIVENESS OF INFRASTRUCTURE DEVELOPMENT ON POVERTY LEVELS IN TANGERANG REGENCY IN 2024 Fitriawati, Andi; Virhafiyanti, Yunita; Madonna, Nora
VARIANCE: Journal of Statistics and Its Applications Vol 7 No 2 (2025): VARIANCE: Journal of Statistics and Its Applications
Publisher : Statistics Study Programme, Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Pattimura

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/variancevol7iss2page175-186

Abstract

Poverty is defined as a condition in which a portion of the population lives with a monthly per capita expenditure below the poverty line. Addressing poverty remains a major challenge for sustainable development, and one strategic approach is infrastructure development. This study analyzes the effectiveness of education, health, and transportation infrastructure, as independent variables, in reducing poverty, as a dependent variable, in Tangerang Regency in 2024. The study employs multiple linear regression because it allows the simultaneous examination of the relationship between a single dependent variable and multiple independent variables. The results indicate that the three infrastructure variables simultaneously significantly affect poverty levels, as shown by an F-statistic of 3.572 and a p-value of 0.02813 at the 5% significance level. The coefficient of determination (R²) of 0.3001 suggests that infrastructure development explains 30.01% of poverty reduction, while other factors influence the remaining 69.99%. However, the partial test results show that none of the infrastructure variables individually has a significant effect on poverty. These findings suggest that infrastructure development contributes to poverty alleviation, though its sectoral impact remains limited. Enhancing equity and improving quality across infrastructure sectors are therefore essential to maximize and broaden its benefits.
Co-Authors Amris Amris Ayu Sofia Bustan, Ariestha Widyastuty Bustan, Ariestha Widyastuty Dani Al Mahkya Dani Al Makhya Dian Anggraini Dian Anggraini Dian Anggraini Dian Anggraini Dila Tirta Julianty Dina Prariesa Dwi Mahrani Fuji Lestari Karina Ayudhia Sasmito Listiani, Amalia Madonna, Nora Mayawi Nurhayati Radot Mh Siahaan Radot MH Siahaan Radot MH Siahaan Rivai, Muklas Salmin, Munazat Shulhany M, Ahmad Siahaan, Radot MH Virhafiyanti, Yunita Werry Febrianti Yoshua Yeremy Budiman