Ahmad Sohaib, Hussain Sardar, Al Mutairi Aned, Kamal Mustafa, Rehman Masood Ur, SidAhmed Mustafa Manahil
Department of Statistics, Abdul Wali Khan University, Mardan, Pakistan.
Department of Statistics, Quaid-i-Azam University, Islamabad, Pakistan.
Heliyon. 2024 Jan 11;10(2):e24115. doi: 10.1016/j.heliyon.2024.e24115. eCollection 2024 Jan 30.
In this article, our main aim is to suggest enhanced families of estimators for estimating the population distribution function (DF) using twofold auxiliary evidence within the framework of simple random sampling. Numerical analysis is performed on four different actual data sets. The precision of the estimators is further investigated exhausting a simulation study. As equated with existing estimators, the suggested families of estimators have minimum mean square error (MSE) and higher percentage relative efficiency (PRE). The succeeding recommended family of estimators outperforms the first family of estimators across all data sets. These are positive indicators of its performance. The theoretical result shows that the recommended family of estimators performs better than the existing estimators. The extent of improvement in efficiency is noteworthy, indicating the superiority of the suggested estimators in terms of minimum MSE.
在本文中，我们的主要目的是提出增强型估计量族，用于在简单随机抽样框架内利用双重辅助证据估计总体分布函数（DF）。对四个不同的实际数据集进行了数值分析。通过模拟研究进一步考察了估计量的精度。与现有估计量相比，所提出的估计量族具有最小均方误差（MSE）和更高的相对效率百分比（PRE）。后续推荐的估计量族在所有数据集上均优于第一个估计量族。这些都是其性能的积极指标。理论结果表明，推荐的估计量族比现有估计量表现更好。效率提高的程度值得注意，表明所建议的估计量在最小均方误差方面具有优越性。
