Muhammad Fajar
Institutu Teknologi Sepuluh Nopember, Badan Pusat Statistik

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A Functional Form of The Zenga Curve Based on Rohde’s Version of the Lorenz Curve Muhammad Fajar; Setiawan; Nur Iriawan; Eko Fajariyanto
Jurnal Matematika MANTIK Vol. 8 No. 1 (2022): April - June
Publisher : Mathematics Department, Faculty of Science and Technology, UIN Sunan Ampel Surabaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15642/mantik.2022.8.1.63-67

Abstract

The Zenga curve is a tool to measure income inequality that represents the income ratio between the bottom income group and the top income group. A proper Zenga curve is a Zenga curve that can detect variations in the Ratio. In this paper, we derive the functional form of the Zenga curve from Rohde's Lorenz curve model. The result of this paper is that the functional form of the Zenga curve from Rohde's version of the Lorenz curve model is a constant. It cannot represent the truly happening phenomenon of inequality.
Pemodelan Kurva Engel Non Makanan dengan Bayesian Quantile Regression di Provinsi Papua Muhammad Fajar; Setiawan
Statistika Vol. 22 No. 1 (2022): Statistika
Publisher : Department of Statistics, Faculty of Mathematics and Natural Sciences, Universitas Islam Bandung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29313/statistika.v22i1.335

Abstract

ABSTRAK Tujuan paper ini adalah untuk melakukan pemodelan kurva Engel non makanan, dimana pada sebaran data mengindikasikan terjadinya heterokedastisitas. Metode yang digunakan dalam penelitian ini adalah regresi kuantil dengan pendekatan Bayesian. Sumber data yang digunakan adalah data pengeluaran konsumsi rumah tangga dan pengeluaran konsumsi rumah tangga untuk non makanan di Provinsi Papua, yang berasal dari SUSENAS Maret 2018. SUSENAS adalah salah satu survei yang dilaksanakan Badan Pusat Statistik. Rumah tangga sampel SUSENAS Maret 2018 sebanyak 10629 rumah tangga. Hasil dari penelitian ini adalah regresi kuantil Bayesian jauh lebih representatif karena mencakup sebaran data, baik pada sentral data maupun daerah disekitar sentral data, dibandingkan regresi linear biasa, dimana regresi linear biasa hanya mencakup berkisar pada sentral data. Ini berimplikasi bahwa pemodelan kurva Engel dengan regresi kuantil adalah sangat cocok dengan sebaran data. Pengeluaran konsumsi rumah tangga berpengaruh positif dan signifikan pada pengeluran konsumsi rumah tangga untuk non makanan. Proporsi pengeluaran konsumsi rumah tangga untuk non makanan berbeda-beda untuk setiap tingkat pengeluarannya. Semakin tinggi pengeluaran rumah tangga, maka proporsi konsumsi untuk non makanan, semakin besar proporsinya. Dan sebaliknya, rumah tangga dengan level pengeluaran rendah, Proporsi konsumsi untuk makan dan minum lebih besar daripada konsumsi untuk non makanan. ABSTRACT This paper aims to model a non-food Engel curve, where the distribution of data shows heteroscedasticity. The method used in this research is quantile regression with the Bayesian approach. The data sources used are household consumption expenditure data and household nonfood consumption expenditures in Papua Province which are derived from SUSENAS March 2018. SUSENAS is one of the surveys conducted by the Badan Pusat Statistik-Statistics Indonesia. SUSENAS March 2018 sample households were 10629 households. The result of this study is that Bayesian quantile regression is much more representative covering the distribution of data, both in the data center and around it, compared to ordinary linear regression, where ordinary linear regression only has a wide range because of the central data. This implies that the modeling of the Engel curve with quantile regression is very suitable for the distribution of the data. Household consumption expenditure has a positive and significant effect on non-food household consumption expenditure. The proportion of household consumption expenditure on food varies for each level of competition. The higher the household expenditure, the higher the proportion of non-food consumption. And conversely, in households with low levels of expenditure, the proportion of consumption for food is greater than consumption for non-food.