Zaagan Abdullah A, Verma Mukesh Kumar, Mahnashi Ali M, Yadav Subhash Kumar, Ahmadini Abdullah Ali H, Meetei Mutum Zico, Varshney Rahul
Department of Mathematics, College of Science, Jazan University, P.O. Box 114, Jazan, 45142, Kingdom of Saudi Arabia.
Department of Statistics, Babasaheb Bhimrao Ambedkar University, Lucknow, 226025, India.
Heliyon. 2024 May 17;10(10):e31291. doi: 10.1016/j.heliyon.2024.e31291. eCollection 2024 May 30.
Improvement in the estimation of population mean has been an area of interest in sampling theory. So many estimators have been suggested for elevated estimation of the population mean in stratified random sampling, but there is still a gap for more closely estimating the population mean. In this paper, the authors propose a ratio-product-cum-exponential-cum-logarithmic type estimator for the enhanced estimation of population mean by implying one auxiliary variable in stratified random sampling using conventional ratio, exponential ratio, and logarithmic ratio type estimators. The suggested estimator is a generalization of ratio, exponential ratio, and logarithmic ratio type estimators, and therefore these are special cases of the proposed estimator. The proposed estimator's bias and MSE are determined and compared with those of influential estimators, with the linear cost function being used to investigate and compare alternatives. Use Cramer's rule to determine the optimal value of the proposed estimator. The proposed estimator is more effective than other existing estimators, according to theoretical observations. For various applications, we suggest using a proposed estimator with the minimal MSE, which is verified by a numerical example, to have practical applicability of theoretical conclusions in real life.
总体均值估计的改进一直是抽样理论中的一个研究热点。在分层随机抽样中，已经提出了许多用于提高总体均值估计的估计量，但在更精确地估计总体均值方面仍存在差距。在本文中，作者通过在分层随机抽样中引入一个辅助变量，利用传统的比率、指数比率和对数比率型估计量，提出了一种比率-乘积-累积-指数-累积-对数型估计量，用于增强总体均值的估计。所提出的估计量是比率、指数比率和对数比率型估计量的推广，因此这些都是所提出估计量的特殊情况。确定了所提出估计量的偏差和均方误差，并与有影响力的估计量进行了比较，使用线性成本函数来研究和比较备选方案。使用克莱姆法则确定所提出估计量的最优值。根据理论观察，所提出的估计量比其他现有估计量更有效。对于各种应用，我们建议使用具有最小均方误差的所提出估计量，通过一个数值例子验证了这一点，以使理论结论在现实生活中具有实际适用性。
