Efficiency of Ratio, Product, and Regression Estimators under Maximum and Minimum Values, Using Two Auxiliary Variables

Abdullah Y Al-Hossain,Mursala Khan

doi:10.1155/2014/693782

Abdullah Y Al-Hossain, Mursala Khan

Open Access

https://doi.org/10.1155/2014/693782

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Abstract

To obtain the best estimates of the unknown population parameters have been the key theme of the statisticians. In the present paper we have suggested some estimators which estimate the population parameters efficiently. In short we propose a ratio, product, and regression estimators using two auxiliary variables, when there are some maximum and minimum values of the study and auxiliary variables, respectively. The properties of the proposed strategies in terms of mean square errors (variances) are derived up to first order of approximation. Also the performance of the proposed estimators have shown theoretically and these theoretical conditions are verified numerically by taking four real data sets under which the proposed class of estimators performed better than the other previous works.

Highlights

In the literature of survey sampling, the use of ancillary information provided by auxiliary variables was discussed by various statisticians in order to improve the efficiency of their constructed estimators or to obtain improved estimators for estimating some most common population parameters, such as population mean, population total, population variance, and population coefficient of variation
Mouatasim and Al-Hossain [9] have studied reduced gradient method for minimax estimation of a bounded poisson mean in which concept of auxiliary variables can be placed and study
We have developed some ratio, product, and regression estimators under maximum and minimum values using two auxiliary variables

Summary

Introduction

In the literature of survey sampling, the use of ancillary information provided by auxiliary variables was discussed by various statisticians in order to improve the efficiency of their constructed estimators or to obtain improved estimators for estimating some most common population parameters, such as population mean, population total, population variance, and population coefficient of variation. In such a situation, ratio, product, and regression estimators provide better estimates of the population parameters.

Proposed Estimators

Comparison of Estimators

Numerical Illustration

Conclusion and Future Work