Comparing Calibration Product Type Estimators of Population Mean In Stratified Sampling under Two Constraints Using Different Distance Measures

Calibration approach adjusts the original design weights by incorporating an auxiliary variable into it, to make the estimator be in the form of a regression estimator. This method was employed to propose calibration product type estimators using three distance measures namely; chi-square distance measure, the minimum entropy distance measure and the modified chi-square distance measure using double constraints. The estimators of variances of the proposed estimators were also obtained. An empirical study to ascertain the performance of these estimators using a secondary data set and simulated data under underlying distributional assumptions of Gamma, Normal and Exponential distributions with varying sample sizes of 10%, 15%, 20% and 25% were carried out. The result with the real life data showed that the calibration product type estimator from chi-square distance measure estimated the population mean with minimum bias than and obtained from the other distance measures. The result from real life data also revealed that the estimator obtained from chi-square distance measure under two constraints was more efficient than the other three estimators. The result from simulation studies showed that the proposed calibration product type estimators outperform the conventional product type estimator in term of efficiency, consistency and reliability under the Gamma and Exponential distributions with the exponential distribution taking the lead. The conventional product type estimator however was found to be better under normal distribution. It was also observed that as sample size increases there was no significant change in the performance of these proposed estimators which justifies the preference with small sample size.