Combination of memory type ratio and product estimators under extended EWMA statistic with application to wheat production.

The extended exponential weighted moving average (EEWMA) statistic is a memory type statistic that uses past observations along with the current information for the estimation of a population parameter to improve the efficiency of the estimators. This study utilized the EEWMA statistic to estimate the population mean with a suitable auxiliary variable. The ratio and product estimators are proposed for the surveys that are time-based by using current information along with that information. The approximate mean square errors are computed for the proposed memory type estimators and mathematical comparison is discussed to demonstrate the efficiency of the estimator. The simulation study was carried out to evaluate the performance of the proposed memory type estimators. It can be seen from the results that the efficiency of the estimator enhances by utilizing the current sample as well as past information. A real-life example is presented to illustrate the usage of proposed estimators.