A Class of Ratio-Type Estimator Using Two Auxiliary Variables for Estimating The Population Mean With Some Known Population Parameters

Toluwalase Janet Akingbade,Fabian C Okafor

doi:10.18187/pjsor.v15i2.2558

Toluwalase Janet Akingbade, Fabian C Okafor

Open Access

https://doi.org/10.18187/pjsor.v15i2.2558

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Abstract

In this paper, we have suggested a class of ratio type estimators with a linear combination using two auxiliary variables with some known population mean of the study variable. The bias and the mean square error of the proposed estimators are derived. We identified sub-members of the class of ratio type estimators. The condition for which the the proposed the proposed estimators perform better than the sample mean per unit, Olkin (1958) multivariate ratio, classical linear regression estimator, Singh(1965), Mohanty (1967) and Swain (2012) are derived. From the analysis, it is observed that the proposed estimators perform better than the sample mean per unit and other existing ratio type estimators considered in this study.

Highlights

It is well known that efficient use of auxiliary variable improves the performance of ratio estimators
For example Tripathi and Khare (1994), Sisodia and Dwivedi (1981), Upadhyaya and Singh (1999), Singh and Tailor (2004), Kadilar and Cingi (2004,2006), Singh and Kakran (1993),Singh and Tailor (2003), Yan and Tian (2010), Subramani and Kumarapandiyan (2012a,2012b, 2012c, 2013), Jelani et al (2013), Raja et al (2017) and Abid et al (2016) have proposed some ratio type estimators based on single auxiliary variable and they showed that their estimators were more efficient than the classical ratio estimator in some cases
Mohanty (1967) proposed ratio estimator using linear combination of the study variable and one of the auxiliary variables for estimating the population mean of the study variable

Summary

Introduction

It is well known that efficient use of auxiliary variable improves the performance of ratio estimators. With the aim of improving on the classical ratio estimator by (Cochran 1977, p151), many authors have suggested some ratio type estimators with known population parameters using single auxiliary variable. We may have prior information on two or more auxiliary variables that can be used to improve the estimation of the population mean of the study variable. Olkin (1958) was the first author to propose ratio estimator with multi-auxiliary variables to improve estimation. For estimating the population mean Yof the study variable y, a simple random sample of size n is selected without replacement from the population S. Mohanty (1967) proposed ratio estimator using linear combination of the study variable and one of the auxiliary variables for estimating the population mean of the study variable.

The proposed Estimator

Sub members of the Class

Efficiency Comparison

Empirical Study

Conclusion