Calibration Ratio Estimators of Population Mean Using Median of Auxiliary Variable

Abstract

In this study we propose a calibration ratio estimator and a calibration separate ratio-product estimator of population mean of study variable under stratified sampling using the median of auxiliary variable. The calibration estimator used calibrated weight determined to minimize a chi-square distance measure subject to a set of constraint related to the auxiliary variable in other to increase precision of the estimators. The median of the auxiliary variable was used in defining the calibration constraints. The variances of the proposed estimators were also obtained. An empirical study to ascertain the performance of these estimators using simulated data under underlying distribution assumption of Student-T distribution, Cauchy distribution, Lognormal distribution, and Standard normal distribution with varying sample sizes of 10%, 20%, and 25% were carried out. The result of simulation reveals that when the underlying distribution is Student-T, at 10% sample size, the efficiency performance of the proposed calibration separate ratio-product estimator is better than other competing estimators. As the sample size is increased to 20% and 25%, the efficiency performance of the existing stratified ratio estimator and existing calibration ratio estimator respectively become better than the other estimators. Under the skewed distributions (Cauchy and Lognormal) and the standard normal distribution, it is observed that the proposed calibration ratio estimator is better than other competing estimators in terms of efficiency, consistency and reliability. The result also reveals that under the lognormal distribution, the conventional stratified ratio estimator and the conventional calibration ratio estimator give the same result.