The use of auxiliary variable is common at estimation stage in the form of ratio and product type estimators. All such estimators use the current sample information to estimate the population characteristics. In this study, we utilized the past samples information along with the current sample information in the form of hybrid exponentially weighted moving averages to construct memory type ratio and product estimators for time-based surveys. The mean square error expressions of the proposed estimators are derived and mathematical conditions are established to prove the efficiency of proposed estimators. An extensive simulation study is conducted to examine the performance of the proposed estimators. It is revealed from the results that use of past sample information along with the current sample excels the performance of estimator in terms of efficiency. A real life example is given to demonstrate the use of proposed estimators.

中文翻译：

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基于时间的调查的人口平均值的记忆类型比率和产品估计量

辅助变量的使用在估计阶段以比率和产品类型估计量的形式很常见。所有这些估计器都使用当前样本信息来估计总体特征。在这项研究中，我们以混合指数加权移动平均线的形式利用过去的样本信息和当前的样本信息来构建基于时间的调查的记忆类型比率和产品估计量。推导出了所提出的估计量的均方误差表达式，并建立了数学条件来证明所提出的估计量的有效性。进行了广泛的模拟研究以检查建议的估计器的性能。结果表明，使用过去样本信息和当前样本在效率方面优于估计器的性能。给出了一个现实生活中的例子来演示建议的估计量的使用。