A Modified Generalized Chain Ratio in Regression Estimator

Abstract

Generalized Chain ratio in regression type estimator is efficient for estimating the population mean. Many authors have derived a Generalized Chain ratio in regression type estimator. However, the computation of its Mean Square Error (MSE) is cumbersome based on the fact that several iterations have to be done, hence the need for a modified generalized chain ratio in regression estimator with lower MSE. This study proposed a modified generalized chain ratio in regression estimator which is less cumbersome in its computation. Two data sets were used in this study. The first data were on tobacco production by tobacco producing countries with yield of tobacco (variable of interest), area of land and production in metric tonnes as the auxiliary variables. The second data were the number of graduating pupils (variable of interest) in Ado-Odo/Ota local government, Ogun state with the number of enrolled pupils in primaries one and five as the auxiliary variables. The mean square errors in the existing and proposed estimators for various values of alpha were derived and relative efficiency was determined. The MSE for the existing estimator of tobacco production gave six values 0.0080, 0.0079, 0.0080, 0.0082, 0.0087 and 0.0093 with 0.0079 as the minimum while the proposed estimator gave 0.0054. The MSEs for the existing estimator for the graduating pupils were 20.73, 11.08, 7.49, 9.96, 18.50 and 33.10 with 7.49 as the minimum while the proposed was 6.52. The results of this study showed that the proposed estimator gave lower MSE for the two data sets, hence it is more efficient.