Efficient estimation combining exponential and ln functions under two phase sampling

AIMS Mathematics

Yasir Hassan¹  Muhammad Ismail¹  Will Murray²  Muhammad Qaiser Shahbaz³ 

[1] 1 Department of Statistics, COMSATS University Islamabad, Lahore Campus, Lahore, Pakistan;2 Department of Mathematics and Statistics, California State University, Long Beach, USA;3 Department of Mathematics and Statistics, King Abdulaziz University, Jeddah, Saudi Arabia;

关键词: auxiliary variables;    two phase sampling;    exponential;    mean square error (mse);   

DOI  :  10.3934/math.2020486

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown