Improving Efficiencies of Ratio- and Product-type Estimators for Estimating Population Mean for Time-based Survey

Abstract

Statisticians often use auxiliary information at an estimation stage to increase efficiencies of estimators. In this article, we suggest modified ratio- and product-type estimators utilizing the known value of the coefficient of variation of the auxiliary variable for a time-based survey. Further, to excel the performance of the suggested estimators, we utilize information from the past surveys along with the current surveys through hybrid exponentially weighted average. We obtain expressions for biases and mean square errors of the suggested estimators. The conditions, under which the suggested estimators have less mean square errors than that of other existing estimators, are also obtained. The results obtained through an empirical analysis examine the use of information from past surveys along with current surveys and show that the mean square errors and biases of the suggested estimators are less than that of the existing estimators. For example: for a sample size 5, mean square error and bias of the suggested ratio-type estimator are (0.0414,0.0065) which are less than (0.5581,0.0944) of the existing Cochran (1940) estimator, (0.4788,0.0758), of Sisodia and Dwivedi (1981) estimator and (0.0482,0.0082) of Muhammad Noor-ul-Amin (2020) estimator. Similarly, mean square error and bias of the suggested product- type estimator are (0.0025,−0.0006) which are less than (0.0612,−0.0096) of the existing Murthy (1964) estimator, (0.0286,−0.0071), of Pandey and Dubey (1988) estimator and (0.0053,−0.0008) of Muhammad Noor-ul-Amin (2020) estimator.