On distribution function under two-phase stratified sampling using two auxiliary variables for mean estimation

We suggest a new class of difference-type estimators under two-phase stratified sampling when using information from two auxiliary variables including their distribution functions. The bias and MSE expressions are derived up to first degree of approximations. It is observed that the proposed class of difference-type estimators is more efficient as compared to the estimators: sample mean, ratio, exponential-ratio, traditional difference-types, Chand, Singh and Choudhury, and Anieting and Ezugwu regression type. The comparisons are made in Section 4 and results based on real data sets and simulation are given in Section 5. It is observed that the performances of the generalized class of estimators is remarkable.