Enhanced Estimation of the Population Mean Using Two Auxiliary Variables under Probability Proportional to Size Sampling

Abstract

In some situations, the population of interest differs significantly in size, for example, in a medical study, the number of patients having a specific disease and the size of health units may vary. Similarly, in a survey related to the income of a household, the household may have a different number of siblings, and then in such situations, we use probability proportional to size sampling. In this article, we have proposed an improved class of estimators for the estimation of population mean on the basis of probability proportional to size (PPS) sampling, using two auxiliary variables. The mathematical expressions of the bias and mean square error (MSE) are derived up to the first order of approximation. Four real datasets and a simulation study are conducted to assess the efficiency of the improved class of estimators. It is found from the real datasets and a simulation study, that the proposed generalized class of estimators produced better results in terms of minimum MSE and higher PRE, as related to other considered estimators. An empirical study is given to support the theoretical results. The theoretical study also demonstrates that the proposed generalized class of estimators outperforms the existing estimators.