An Efficient Ratio-Cum-Exponential Estimator for Estimating the Population Distribution Function in the Existence of Non-Response Using an SRS Design

Abstract

To gain insight into various phenomena of interest, cumulative distribution functions (CDFs) can be used to analyze survey data. The purpose of this study was to present an efficient ratiocum-exponential estimator for estimating a population CDF using auxiliary information under two scenarios of non-response. Up to first-order approximation, expressions for the bias and mean squared error (MSE) were derived. The proposed estimator was compared theoretically and empirically, with the modified estimators. The proposed estimator was found to be better than the modified estimators based on present-relative efficiency PRE and MSE criteria under the specific conditions.

Keywords

• auxiliary information
• exponential estimator
• sub-sampling of non-respondents
• cumulative distribution function
• non-response