A Simulation Study: Population Distribution Function Estimation Using Dual Auxiliary Information under Stratified Sampling Scheme

Abstract

In survey sampling, information on auxiliary variables related to the main variable is often available in many practical problems. Since the mid-twentieth century, researchers have taken a keen interest in the use of auxiliary information, due to its usefulness in estimation methods. In this article, our main objective is to discover the problem associated with estimation of the finite population distribution function, using the known auxiliary variable, which occurs as the sample distribution function and the rank of the auxiliary variable. A new family of the finite population distribution function estimators is proposed in the stratified sampling scheme. The mathematical equations for the bias and mean square error have been obtained for each proposed estimator, along with the efficiency conditions. Besides theoretical efficiency comparison, an empirical study has also been conducted to analyze the performance of estimators. A simulation study is also performed to observe the efficiency of the proposed estimators. The implementation of the proposed sampling scheme is illustrated by a practical example.

New generalized class of estimators for estimation of finite population mean based on probability proportional to size sampling using two auxiliary variables: A simulation study

“…The proposed estimator is more robust as compared to ratio, product and regression estimators as it can take any type of data that exists in literature. Taking motivation from Ahmad et al, 51,52 we propose a new class of estimators using two auxiliary variables under PPS sampling. wherewhere Ψ18 and Ψ19 are the unknown constants, a and b are described earlier. Some family members of estimators are given in Table 1.…”

“…The proposed estimator is more robust as compared to ratio, product and regression estimators as it can take any type of data that exists in literature. Taking motivation from Ahmad et al, 51,52 we propose a new class of estimators using two auxiliary variables under PPS sampling.…”