Hussain Mujeeb, Zaman Qamruz, Ahmad Hijaz, Albalawi Olayan, Iftikhar Soofia
Department of Statistics, University of Peshawar, Pakistan.
Near East University, Operational Research Center in Healthcare, TRNC Mersin 10, Nicosia, 99138, Turkey.
Heliyon. 2024 May 18;10(10):e31529. doi: 10.1016/j.heliyon.2024.e31529. eCollection 2024 May 30.
This paper contributes to the existing literature on variance estimators by utilizing supplementary information. The variance estimation problem of a finite population is a significant matter as sometimes, it is tough to control the variation. For this purpose, an optimum family of exponential variance estimators is suggested under simple random sampling. Moreover, different specific members of the proposed estimators are identified by incorporating various known characteristics of the supplementary variable in the suggested generalized class of estimators. The derivations for the expressions of bias as well as mean square error (MSE) of the proposed estimators are conducted. The suggested family of estimators is studied in different situations by using sets of real data and simulation studies for their performance. To evaluate the efficiency of the suggested estimators, R software is used for the analysis. The study compares the performance of the proposed estimators against the traditional estimators. The theoretical and numerical comparisons show that the estimators suggested in the study are superior in efficiency as compared to the existing estimators.
本文通过利用补充信息，为现有关于方差估计量的文献做出了贡献。有限总体的方差估计问题是一个重要问题，因为有时很难控制变异。为此，在简单随机抽样下提出了一个最优的指数方差估计量族。此外，通过在建议的广义估计量类中纳入补充变量的各种已知特征，确定了所提出估计量的不同特定成员。对所提出估计量的偏差和均方误差（MSE）表达式进行了推导。通过使用实际数据集和模拟研究来考察所提出估计量族在不同情况下的性能。为了评估所提出估计量的效率，使用R软件进行分析。该研究将所提出估计量的性能与传统估计量进行了比较。理论和数值比较表明，该研究中提出的估计量在效率上优于现有估计量。
