Some classes of exponential ratio-type imputation estimators of population distribution in the presence of measurement error

Abstract

This study proposes a new class of exponential ratio-type imputation estimators for estimating the population distribution function under non-response and measurement error. The aim is to improve accuracy by reducing bias and mean squared error (MSE), while also checking efficiency and precision. Theoretical properties were derived, and numerical illustrations were carried out using real survey data. Four measures were used to judge performance: MSE to compare efficiency between existing and proposed estimators, Percentage Relative Efficiency (PRE) to evaluate efficiency per estimator, Absolute Relative Bias (ARB) to measure the level of bias in estimation, and Percentage Relative Loss in Precision (PRLP) to assess precision loss within the proposed class. The results show that the proposed estimators consistently record lower MSE values than existing ones, proving they are more efficient. PRE values are higher than 100 for most cases, confirming strong efficiency gains per estimator. ARB values are very small and generally lower for the proposed estimators, showing that they reduce bias effectively. Although PRLP indicates some precision loss, the proposed estimators keep it at a lower and acceptable level. Overall, the proposed estimators outperform existing ones and provide a more reliable approach for handling survey data with non-response and measurement error.