An improved class of predictive estimators of population distribution function in the presence of non-response

Abstract

In the present work, we have proposed a novel general class of estimators for the estimation of population distribution function in two distinct situations of non-response. The estimation of distribution function (DF) may play an important role in environmental sciences such as in modelling the annual data of atmospheric NOx temporal concentration, drug removal rates from the body, to present the distribution of gene expression levels across cells etc. Similarly, it may also be useful in other environmental data like groundwater quality, rainfall, wind speed, river discharges, etc. for effective analysis leading to predictive modelling. In this study, it is shown that the suggested estimators of DF are among the best of all other considered estimators. Some estimators are also derived from the proposed family by choosing the suitable values of constants used. Theoretical comparisons of the proposed family of estimators with other family of estimators have been discussed. An empirical study based on two real data sets from literature has been conducted where it has been found that the performance of the proposed family of estimators is superior in terms of enhanced percentage relative efficiencies (PREs) than other family of estimators considered in this study. Further, a simulation study is also carried out which validates the competency behaviour of suggested estimators.

Keywords

• Cumulative distribution function
• Study variable
• Auxiliary variable
• Relative efficiency
• Absolute bias
• Non-response