Statistical Computation of Population Proportion by Developing Enhanced Generalized Class of Estimators

Abstract

One of the key issues in the survey sampling and statistical inference is the estimation of population proportion. In this research the generalized form of estimators is suggested to estimate the proportions of the population using the addition of auxiliary properties which show correlation with the research variable. The suggested course of action involves and generalizes old ratio, product and regression-like estimators, thus offering a single and adaptable estimation of proportions. The bias and the mean squared error (MSE) of the proposed estimators are expressed up to the first-order approximation, which makes it easier to determine their efficiency. The effectiveness of the estimators is also checked with different conditions with the help of numerical examples on the basis of real data sets. The findings indicate that the proposed estimators are better than the conventional estimators in terms of MSE in case of a strong correlation between the study variable and auxiliary attributes. Additionally, this paper provides the best conditions in which the suggested estimators achieve minimum MSE, which can be used in practice. It is due to the flexibility of the generalized framework that practitioners are able to choose or develop effective estimators specific to particular survey situations. In general, the suggested methodology does not only add to the theoretical development, but also to the practical enhancement of estimating population proportions with the help of auxiliary information.