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.

Calibration Estimation of Population Proportion in Probability Proportional to Size Sampling in the Presence of Non-Response

“…An improved class of estimators has been obtained for the estimation of population mean based on Probability Proportional to size (PPS) sampling, with the help of two auxiliary variables (4) . The problem of estimating the population mean of the study variable with the help of auxiliary variables under varying probability techniques was focused with and without measurement errors (5) .…”

Estimation of finite population mean using double sampling under probability proportional to size sampling in the presence of extreme values

“…Researchers can investigate this research by looking at [ 17 ] a discussion of using outliers to estimate the average of a population using a probability-based sampling design [ 18 , 19 ]. recommended PPS when outliers are present [ 20 ].…”