A general procedure of estimating the population variance when coefficient of variation of an auxiliary variable is known in sample surveys

This paper deals with the problem of estimating population variance <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${{S}_{\rm y}^2}$$</EquationSource> </InlineEquation> of the study variable y. We have suggested a family of estimators of population variance <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$${{S}_{\rm y}^2}$$</EquationSource> </InlineEquation> using the transformations on both the study variable and the auxiliary variable when coefficient of variation of an auxiliary variable x is known. The suggested family of estimators is very wide from which we can generate many estimators by putting the suitable values of scalars. The bias and mean squared error have been obtained upto the first order of approximation. The empirical study is carried out to the support of the suggested family of estimators. Copyright Springer Science+Business Media B.V. 2013