Sher Khazan, Ameeq Muhammad, Hassan Muhammad Muneeb, Albalawi Olayan, Afzal Ayesha
Department of Statistics University of Peshawar, Pakistan.
Department of Statistics, The Islamia University Bahawalpur, Punjab, Pakistan.
Heliyon. 2024 May 9;10(10):e30991. doi: 10.1016/j.heliyon.2024.e30991. eCollection 2024 May 30.
In general, the incorporation of supplementary information reduces the Mean Square Error (MSE) and, consequently, enhances the precision of estimating a population parameter. This improvement relies on the appropriate application of a suitable function, with careful consideration. This study introduces two innovative families of estimators for the finite population mean, both of which exhibit superior performance in scenarios involving dual auxiliary information in simple random sampling. Expressions up to the first-order approximation, for bias, and Mean Square Error were derived, and the conditions under which these proposed families surpassed the existing estimators. Our evaluation involved the use of both real and simulated data to compute the Mean Square Error and Percent Relative Efficiency (PRE) of the estimators. A comparative analysis revealed that under the specified conditions, both proposed families yielded more precise results.
一般来说，纳入补充信息会降低均方误差（MSE），从而提高估计总体参数的精度。这种改进依赖于合适函数的恰当应用，并需仔细考虑。本研究引入了两个用于有限总体均值的创新型估计量族，在简单随机抽样中涉及双重辅助信息的情况下，这两个估计量族均表现出卓越的性能。推导了偏差和均方误差直至一阶近似的表达式，以及这些提议的估计量族优于现有估计量的条件。我们的评估涉及使用真实数据和模拟数据来计算估计量的均方误差和百分比相对效率（PRE）。比较分析表明，在特定条件下，两个提议的估计量族都产生了更精确的结果。
