Sains Malaysiana 52(7)(2023): 2149-2162

http://doi.org/10.17576/jsm-2023-5207-20

On Some New Exponential Ratio Estimator of Population Mean in Two Phase Sampling

(Beberapa Penganggar Nisbah Eksponen Baharu bagi Min Populasi dalam Persampelan Dua Fasa)

YASIR HASSAN^1,*, MUHAMMAD FAROOQ², SALEHA YASIR³ & WILL MURRAY⁴

¹Lahore Business School, The University of Lahore, Pakistan

²Department of Statistics, COMSATS University Islamabad, Lahore Campus, Lahore, Pakistan

³The University of Lahore, Pakistan

⁴Department of Mathematics and Statistics, California State University, Long Beach, USA

Received: 14 November 2022/Accepted: 12 July 2023

Abstract

In this paper, we suggest employing the exponential ratio estimator to estimate the mean of the study variable using a two-phase sample strategy with two modified auxiliary variables. Several researchers discussed the properties of the estimators they proposed and discovered that the estimators in their studies were relatively efficient. The estimators previously studied are listed chronologically in the appendix to this paper. In two phase sampling, the estimator's mean square errors and relative efficiencies are calculated using auxiliary variable information. To assess the properties of our proposed estimator, we noticed that it has a lower mean square error (MSE) than the classical ratio estimator and some other exponential ratio estimators. The estimator is more useful than other estimators in solving real-world issues, notably in engineering, environmental science, management, and biological sciences. The proposed estimator has been applied to real-world data sets such as BRICS, Son's Head Measurement, Number of Hospital Beds, Sale Price of Residence, Ambient Pressure (AP), and Heating Load. In survey research, our suggested estimator has also been demonstrated to be more effective.

Keywords: Auxiliary variable; exponential; mean square error; two phase

ABSTRAK

Dalam makalah ini, kami mencadangkan penggunaan penganggar nisbah eksponen untuk menganggar min pemboleh ubah kajian menggunakan strategi sampel dua fasa dengan dua pemboleh ubah tambahan yang diubah suai. Beberapa penyelidik membincangkan sifat penganggar yang mereka cadangkan dan mendapati bahawa penganggar dalam kajian mereka adalah agak cekap. Penganggar yang dikaji sebelum ini disenaraikan secara kronologi dalam lampiran kertas ini. Dalam persampelan dua fasa, ralat purata kuasa dua penganggar dan kecekapan relatif dihitung menggunakan maklumat pemboleh ubah tambahan. Untuk menilai sifat penganggar yang dicadangkan ini, kami mendapati ia mempunyai ralat min kuasa dua (MSE) yang lebih rendah daripada penganggar nisbah klasik dan beberapa penganggar nisbah eksponen lain. Penganggar ini lebih baik daripada penganggar lain dalam menyelesaikan isu dunia sebenar, terutamanya dalam kejuruteraan, sains alam sekitar, pengurusan dan sains biologi. Penganggar yang dicadangkan telah digunakan pada set data dunia sebenar seperti BRICS, Ukuran Kepala Anak, Bilangan Katil Hospital, Harga Jualan Kediaman, Tekanan Ambien (AP) dan Beban Pemanasan. Dalam kajian tinjauan, penganggar cadangan kami juga telah ditunjukkan sebagai lebih berkesan.

Kata kunci: Eksponen; pemboleh ubah bantu; purata kuasa dua; ralat dua fasa

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*Corresponding author; email:yasirhassan7924@gmail.com