Variance estimation using Bernoulli auxiliary variable for time-scaled survey

The diversity in the qualities under investigation is necessary to comprehend any phenomenon, whether in a real-world or practical setting. It is crucial to know the differences between current and previous circumstances. Therefore, to estimate the population variance with dichotomous auxiliary information, the exponentially weighted moving average statistic is used. This manuscript suggests a generalized class of memory-type estimators for the estimation of population variance using the Bernoulli auxiliary variable under time-scaled survey. The properties of the suggested class of memory type estimator and exponentially weighted moving average version of the usual ratio, regression, and exponential estimators are derived up to the first order of approximation. It has been shown through empirical and simulation study that the suggested estimator is more efficient than the usual estimators and the exponentially weighted moving average version of the estimators in the literature.