Zahid Rashiqa, Noor-Ul-Amin Muhammad, Khan Imad, AlQahtani Salman A, Pathak Pranav Kumar, Rahimi Javed
COMSATS University Islamabad-Lahore Campus, Lahore, Pakistan.
Department of Statistics, Abdul Wali Khan University Mardan, Mardan, Pakistan.
Sci Rep. 2023 Aug 20;13(1):13547. doi: 10.1038/s41598-023-40687-4.
The extended exponential weighted moving average (EEWMA) statistic is a memory type statistic that uses past observations along with the current information for the estimation of a population parameter to improve the efficiency of the estimators. This study utilized the EEWMA statistic to estimate the population mean with a suitable auxiliary variable. The ratio and product estimators are proposed for the surveys that are time-based by using current information along with that information. The approximate mean square errors are computed for the proposed memory type estimators and mathematical comparison is discussed to demonstrate the efficiency of the estimator. The simulation study was carried out to evaluate the performance of the proposed memory type estimators. It can be seen from the results that the efficiency of the estimator enhances by utilizing the current sample as well as past information. A real-life example is presented to illustrate the usage of proposed estimators.
扩展指数加权移动平均（EEWMA）统计量是一种记忆型统计量，它利用过去的观测值以及当前信息来估计总体参数，以提高估计量的效率。本研究利用EEWMA统计量，通过一个合适的辅助变量来估计总体均值。针对基于时间的调查，利用当前信息以及该信息提出了比率估计量和乘积估计量。计算了所提出的记忆型估计量的近似均方误差，并进行了数学比较以证明估计量的效率。进行了模拟研究以评估所提出的记忆型估计量的性能。从结果可以看出，通过利用当前样本以及过去的信息，估计量的效率得到了提高。给出了一个实际例子来说明所提出估计量的用法。
