Modified Ratio Estimators for Population Means with Two Auxiliary Parameters Using Calibration Weights
Adubi S. Ayodeji
Department of Statistics, University of Nigeria, Nsukka, Nigeria.
Oluwagbenga T. Babatunde *
Department of Statistics, University of Nigeria, Nsukka, Nigeria.
Ude O. Ifeoma
Department of Statistics, University of Nigeria, Nsukka, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
Many researchers have used different auxiliary parameters such as coefficient of variation, coefficient of kurtosis, coefficient of skewness, quartiles, deciles etc., to improve the precision of estimators under various sampling schemes. This paper suggested a class of ratio estimators with two known auxiliary variable parameters for the estimation of population means under a simple random sample without replacement (SRSWOR) using the calibration weighting method. The calibrated weight was obtained using a new calibration constraint, which includes the known standard deviation of the auxiliary variable. The biases and mean square errors of the proposed estimators were derived and compared with the biases and mean square errors of the existing modified ratio estimators in Upadhyaya & Singh [1], Singh [2], Lu & Yan [3], and Yan & Tian [4]. Furthermore, we derived the condition for which the proposed estimators perform better than the existing estimators. The results from using real data sets showed that the suggested estimators perform better than the existing ratio estimators.
Keywords: Calibration, estimator, stratified sampling, ratio, mean square error, bias