Department of Statistics, Abdul Wali Khan University, Mardan, Pakistan.
Foundation University Medical College, Foundation University School of Health Sciences, DHA-I, Islamabad, 44000, Pakistan.
Sci Rep. 2023 Apr 3;13(1):5415. doi: 10.1038/s41598-023-30150-9.
This article aims to suggest a new improved generalized class of estimators for finite population distribution function of the study and the auxiliary variables as well as mean of the usual auxiliary variable under simple random sampling. The numerical expressions for the bias and mean squared error (MSE) are derived up to first degree of approximation. From our generalized class of estimators, we obtained two improved estimators. The gain in second proposed estimator is more as compared to first estimator. Three real data sets and a simulation are accompanied to measure the performances of our generalized class of estimators. The MSE of our proposed estimators is minimum and consequently percentage relative efficiency is higher as compared to their existing counterparts. From the numerical outcomes it has been shown that the proposed estimators perform well as compared to all considered estimators in this study.
本文旨在提出一个新的改进的广义类估计量，用于有限总体分布函数的研究，以及简单随机抽样下辅助变量和常用辅助变量均值的估计。偏差和均方误差（MSE）的数值表达式推导至一阶近似。从我们的广义类估计量中，我们得到了两个改进的估计量。第二个提出的估计量的增益比第一个估计量更大。三个真实数据集和一个模拟实验用于衡量我们的广义类估计量的性能。我们提出的估计量的均方误差最小，因此相对于它们的现有对应物，百分比相对效率更高。从数值结果可以看出，与本研究中所有考虑的估计量相比，所提出的估计量表现良好。
