A Class of Estimators for Population Ratio in Simple Random Sampling Using Variable Transformation

ABSTRACT

This paper is an
extension and generalization of the study carried out by [1] on the estimation of the population ratio (*R*) of the population means of two
variables (*y* and *x*) under Simple Random Sampling (SRS) scheme, using a variable
transformation of the auxiliary variable, *x*.
All the six estimators proposed by [1] are easily
identified as special cases of the proposed class of estimators. Asymptotic
properties of the proposed class of estimators are derived theoretically and
subsequently verified using empirical illustrations. Some of the proposed
estimators are found to have relatively large gains in efficiency over the
customary ratio estimator, for the given data
set.

Cite this paper

Onyeka, A. , Nlebedim, V. and Izunobi, C. (2014) A Class of Estimators for Population Ratio in Simple Random Sampling Using Variable Transformation.*Open Journal of Statistics*, **4**, 284-291. doi: 10.4236/ojs.2014.44029.

Onyeka, A. , Nlebedim, V. and Izunobi, C. (2014) A Class of Estimators for Population Ratio in Simple Random Sampling Using Variable Transformation.

References

[1] Onyeka, A.C., Nlebedim, V.U. and Izunobi, C.H. (2013) Estimation of Population Ratio in Simple Random Sampling Using Variable Transformation. Global Journal of Science Frontier Research, 13, 57-65.

[2] Srivenkataramana, T. (1980) A Dual of Ratio Estimator in Sample Surveys. Biometrika, 67, 199-204. http://dx.doi.org/10.1093/biomet/67.1.199

[3] Singh, H.P. and Tailor, R. (2005) Estimation of Finite Population Mean Using Known Correlation Coefficient between Auxiliary Variables. Statistica, 65, 407-418.

[4] Tailor, R. and Sharma, B.K. (2009) A Modified Ratio-Cum-Product Estimator of Finite Population Mean Using Known Coefficient of Variation and Coefficient of Kurtosis. Statistics in Transition—New Series, 10, 15-24.

[5] Sharma, B. and Tailor, R. (2010) A New Ratio-Cum-Dual to Ratio Estimator of Finite Population Mean in Simple Random Sampling. Global Journal of Science Frontier Research, 10, 27-31.

[6] Onyeka, A.C. (2013) Dual to Ratio Estimators of Population Mean in Post-Stratified Sampling Using Known Value of Some Population Parameters. Global Journal of Science Frontier Research, 13, 13-23.

[7] Singh, M.P. (1965) On the Estimation of Ratio and Product of the Population Parameters. Sankhya, B27, 321-328.

[8] Srivastava, S.R., Khare, B.B. and Srivastaca, S.R. (1988) On Generalized Chain Estimator for Ratio and Product of Two Population Means Using Auxiliary Variables. Assam Statistical Review, 2, 21-29.

[9] Upadhyaya, L.N., Singh, G.N. and Singh, H.P. (2000) Use of Transformed Auxiliary Variable in the Estimation of Population Ratio in Sample Survey. Statistics in Transition, 4, 1019-1027.

[10] Pandey, B.N. and Dubey, V. (1988) Modified Product Estimator Using Coefficient of Variation of Auxiliary Variate. Assam Statistical Review, 2, 64-66.

[1] Onyeka, A.C., Nlebedim, V.U. and Izunobi, C.H. (2013) Estimation of Population Ratio in Simple Random Sampling Using Variable Transformation. Global Journal of Science Frontier Research, 13, 57-65.

[2] Srivenkataramana, T. (1980) A Dual of Ratio Estimator in Sample Surveys. Biometrika, 67, 199-204. http://dx.doi.org/10.1093/biomet/67.1.199

[3] Singh, H.P. and Tailor, R. (2005) Estimation of Finite Population Mean Using Known Correlation Coefficient between Auxiliary Variables. Statistica, 65, 407-418.

[4] Tailor, R. and Sharma, B.K. (2009) A Modified Ratio-Cum-Product Estimator of Finite Population Mean Using Known Coefficient of Variation and Coefficient of Kurtosis. Statistics in Transition—New Series, 10, 15-24.

[5] Sharma, B. and Tailor, R. (2010) A New Ratio-Cum-Dual to Ratio Estimator of Finite Population Mean in Simple Random Sampling. Global Journal of Science Frontier Research, 10, 27-31.

[6] Onyeka, A.C. (2013) Dual to Ratio Estimators of Population Mean in Post-Stratified Sampling Using Known Value of Some Population Parameters. Global Journal of Science Frontier Research, 13, 13-23.

[7] Singh, M.P. (1965) On the Estimation of Ratio and Product of the Population Parameters. Sankhya, B27, 321-328.

[8] Srivastava, S.R., Khare, B.B. and Srivastaca, S.R. (1988) On Generalized Chain Estimator for Ratio and Product of Two Population Means Using Auxiliary Variables. Assam Statistical Review, 2, 21-29.

[9] Upadhyaya, L.N., Singh, G.N. and Singh, H.P. (2000) Use of Transformed Auxiliary Variable in the Estimation of Population Ratio in Sample Survey. Statistics in Transition, 4, 1019-1027.

[10] Pandey, B.N. and Dubey, V. (1988) Modified Product Estimator Using Coefficient of Variation of Auxiliary Variate. Assam Statistical Review, 2, 64-66.