An Alternative Ratio-Cum-Product Estimator of Finite Population Mean Using Coefficient of Kurtosis of Two Auxiliary Variates in Two-Phase Sampling

Balkishan Sharma,Rajesh Tailor

doi:10.18187/pjsor.v10i3.639

Abstract

Normal 0 MicrosoftInternetExplorer4 This paper deals with the problem of estimation of population mean in two-phase sampling. A ratio-product estimator of population mean using known coefficient of kurtosis of two auxiliary variates has been proposed. In fact, it is a two-phase sampling version of Tailor et al. (2010) estimator and its properties are studied. Proposed estimator has been compared with usual unbiased estimator, classical ratio and product estimator in two-phase sampling, and two-phase sampling versions of Singh (1967) and Singh et al. (2004) estimators respectively. To judge the merits of the proposed estimator over other estimators an empirical study is also carried out. /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin:0in; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Times New Roman";}

Highlights

Auxiliary information plays a very important role in improving the efficiencies of estimator(s) of population parameter(s)
Use of coefficient of kurtosis of auxiliary variate has been in practice for improving the efficiency of the estimators of finite population mean
[10]Singh (1967) used information on two auxiliary variates and defined a ratio-product estimator assuming that population mean of auxiliary variates are known

Summary

Introduction

Auxiliary information plays a very important role in improving the efficiencies of estimator(s) of population parameter(s). Assuming that population means X1 and X 2 of the auxiliary variables x1 and x2 are known, [9]Singh et al (2004) defined a ratio and product type estimators using coefficient of kurtosis 2 (x1) and 2 (x2 ) respectively as YSR. Expressions (4.1) to (4.6) are the conditions in which proposed estimator Y T(d) in case II would be more efficient than simple mean estimator y , usual two-phase sampling ratio and product estimators y(d) R and y(d) P versions of estimators suggested by [9]Singh et al (2004) ( YS(Rd) and YS(Pd) ) and [10]Singh (1967) two-phase sampling ratio-product type estimator YS(Rd)P respectively

Empirical Study

Conclusion