Calibration Approach Product Type Estimators of Population Mean in Stratified Sampling with Single Constraint: A Comparison of Three Distance Measures
Enang, Ekaette Inyang
Department of Statistics, University of Calabar, Calabar- Cross River State, Nigeria.
Ojua, Doris Nkan *
Department of Statistics, University of Calabar, Calabar- Cross River State, Nigeria.
T. T. Ojewale
Department of Statistics, University of Calabar, Calabar- Cross River State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
This study employed the method of calibration on product type estimator 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 for single constraint. The estimators of variances of the proposed estimators were also obtained. An empirical study to ascertain the performance of these estimators was carried out using real life and stimulated data set. The result with the real life data showed that the proposed calibration product type estimator produced better estimates of the population mean compared to and . Results from the simulation study showed that the proposed calibration product type estimators had a high gain in efficiency as compared to the product type estimator. The simulation result also showed that the proposed estimators were more consistent and reliable under the Gamma and Exponential distributions with the exponential distribution taking the lead. The conventional product type estimator however was found to be better if the underlying distributional assumption is normal in nature.
Keywords: Finite population, auxiliary variable, stratified sampling, calibration estimators, population mean