Incorporating past data in enhancing coefficient of variation estimation: A practical approach

Measurement of variability is a crucial issue in survey sampling. This problem takes on a practical perspective when considering relative variability, as real-life scenarios often involve comparing two different characteristics or the same characteristic on different scales. For researchers and professionals working in a variety of fields, including agriculture, the stock market, economics, public health, finance, and more, its ability to improve decision-making processes makes it an essential tool. In this paper, we employ the exponentially weighted moving average statistic to propose memory-type estimators for the coefficient of variation that take advantage of auxiliary information in time-scaled surveys. These estimators are based on the concept of memory-type statistics, which integrate both past and present data to enhance the estimation of population parameters. Designed to dynamically incorporate historical data, they improve the accuracy and efficiency of estimation in longitudinal surveys. To validate their effectiveness, we establish the necessary mathematical conditions and explicitly derive expressions for bias and mean square error. Observations from a simulation study indicate that incorporating historical sample data alongside current data significantly enhances estimator performance. In addition, two real-life case studies are presented to demonstrate the efficacy and superiority of the proposed estimators.