Efficient estimation combining exponential and ln functions under two phase sampling

• Published in: AIMS mathematics Vol. 5; no. 6; pp. 7604 - 7622
• Main Authors: Hassan, Yasir, Ismail, Muhammad, Murray, Will, Qaiser Shahbaz, Muhammad
• Format: Journal Article
• Language: English
• Published: AIMS Press 01.01.2020
• Subjects: auxiliary variables; exponential; mean square error (mse); two phase sampling
• ISSN: 2473-6988; 2473-6988
• DOI: 10.3934/math.2020486

In this study, we propose the combination of exponential and ln ratio type estimator to estimate the mean of Y (Study Variable) by incorporating two auxiliary variables in two phase sampling scheme. Under simple random sampling without replacement, the illustration for mean square error and mathematical comparisons are presented. Several approaches are available in literature to estimate the study variable by using information on the variable of interest. The performance of our proposed estimator is compared with other ratio type estimators theoretically and empirically. It is observed that ratio and exponential ratio estimators considered by various researchers and usual unbiased estimator is less efficient than our proposed estimator. An efficiency comparison is also given using five data sets and simulation studies for checking the merits of our proposed estimator and outcomes are sound and moderately illuminating in comparison to different estimators.