Estimation of Finite Population Distribution Function Using Auxiliary Information Under Stratified Random Sampling

Nosheen  Bibi; Kalim  Ullah; Hassan  Zeb; Salman  Arif Cheema; Zawar  Hussain; Alamgir  Khalil

Authors

Nosheen Bibi Department of Statistics Islamia College, Peshawar, Pakistan
Kalim Ullah Department of Anesthesiology, Aga Khan University, Karachi, Pakistan
Hassan Zeb Department of Statistics Islamia College, Peshawar, Pakistan
Salman Arif Cheema Department of Applied Sciences, National Textile University, Faisalabad, Pakistan
Zawar Hussain Department of Statistics, Islamia University Bahawalpur, Pakistan
Alamgir Khalil Department of Statistics, University of Peshawar, Peshawar, Pakistan

Keywords:

Auxiliary information, bias, mean squared error, percentage relative efficiency

Abstract

This paper introduces a set of estimators designed for the estimation of the distribution function of a finite population under the framework of stratified random sampling. These estimators make use of supplementary information, including the mean of the distribution function and the empirical distribution function of an auxiliary variable. To assess the performance of the proposed estimators, we employ a first-order approximation to analyze their biases and mean squared errors. A comprehensive comparative analysis, both theoretically and numerically, is carried out to contrast these new estimators with adapted distribution function estimators. The results indicate that, in terms of mean squared error and percentage relative efficiency, the proposed estimators outperform the adapted estimators.

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