In this study, we propose the combination of exponential and ln ratio type estimator to estimate the mean of Y (Study Variable) by incorporating two auxiliary variables in two phase sampling scheme. Under simple random sampling without replacement, the illustration for mean square error and mathematical comparisons are presented. Several approaches are available in literature to estimate the study variable by using information on the variable of interest. The performance of our proposed estimator is compared with other ratio type estimators theoretically and empirically. It is observed that ratio and exponential ratio estimators considered by various researchers and usual unbiased estimator is less efficient than our proposed estimator. An efficiency comparison is also given using five data sets and simulation studies for checking the merits of our proposed estimator and outcomes are sound and moderately illuminating in comparison to different estimators.

中文翻译：

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两相采样下结合指数函数和ln函数的有效估计

在这项研究中，我们提出将指数和ln比率类型估计器相结合，以通过在两个阶段的采样方案中合并两个辅助变量来估计Y（研究变量）的平均值。在没有替换的简单随机抽样下，给出了均方误差和数学比较的图示。文献中有几种方法可以通过使用有关感兴趣变量的信息来估计研究变量。从理论上和经验上，将我们提出的估算器的性能与其他比率类型的估算器进行比较。可以看出，各种研究人员和通常的无偏估计器所考虑的比率和指数比率估计器比我们提出的估计器效率低。