Estimation of Population Ratio in Post-Stratified Sampling Using Variable Transformation

ABSTRACT

Extending the work carried out by [1], this paper proposes six combined-type estimators of population ratio of two variables in post-stratified sampling scheme, using variable transformation. Properties of the proposed estimators were obtained up to first order approximations,(*on*–^{1}), both for achieved sample configurations (conditional argument) and over repeated samples of fixed size *n* (unconditional argument). Efficiency conditions were obtained. Under these conditions the proposed combined-type estimators would perform better than the associated customary combined-type estimator. Furthermore, optimum estimators among the proposed combined-type estimators were obtained both under the conditional and unconditional arguments. An empirical work confirmed the theoretical results.

Extending the work carried out by [1], this paper proposes six combined-type estimators of population ratio of two variables in post-stratified sampling scheme, using variable transformation. Properties of the proposed estimators were obtained up to first order approximations,(

KEYWORDS

Variable Transformation, Combined-Type Estimator, Ratio, Product and Regression-Type Estimators, Mean Squared Error

Variable Transformation, Combined-Type Estimator, Ratio, Product and Regression-Type Estimators, Mean Squared Error

Cite this paper

Onyeka, A. , Izunobi, C. and Iwueze, I. (2015) Estimation of Population Ratio in Post-Stratified Sampling Using Variable Transformation.*Open Journal of Statistics*, **5**, 1-9. doi: 10.4236/ojs.2015.51001.

Onyeka, A. , Izunobi, C. and Iwueze, I. (2015) Estimation of Population Ratio in Post-Stratified 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] Sukhatme, P.V. and Sukhatme, B.V. (1970) Sampling Theory of Surveys with Applications. Iowa State University Press, Ames.

[3] Cochran, W.G. (1977) Sampling Techniques. 3rd Edition, John Wiley & Sons, New York.

[4] Cochran, W.G. (1940) The Estimation of the Yields of the Cereal Experiments by Sampling for the Ratio of Grain to Total Produce. The Journal of Agricultural Science, 30, 262-275.

http://dx.doi.org/10.1017/S0021859600048012

[5] Robson, D.S. (1957) Application of Multivariate Polykays to the Theory of Unbiased Ratio-Type Estimation. Journal of the American Statistical Association, 52, 511-522.

http://dx.doi.org/10.1080/01621459.1957.10501407

[6] Murthy, M.N. (1964) Product Method of Estimation. Sankhya Series A, 26, 294-307.

[7] Singh, M.P. (1965) On the Estimation of Ratio and Product of the Population Parameters. Sankhya Series B, 27, 321-328.

[8] 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.

[9] Onyeka, A.C., Nlebedim, V.U. and Izunobi, C.H. (2014) A Class of Estimators for Population Ratio in Simple Random Sampling Using Variable Transformation. Open Journal of Statistics, 4, 284-291.

http://dx.doi.org/10.4236/ojs.2014.44029

[10] 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

[11] Singh, H.P. and Tailor, R. (2005) Estimation of Finite Population Mean Using Known Correlation Coefficient between Auxiliary Characters. Statistica, 4, 407-418.

[12] 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.

[13] 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.

[14] Onyeka, A.C. (2012) Estimation of Population Mean in Post-Stratified Sampling Using Known Value of Some Population Parameter(s). Statistics in Transition—New Series, 13, 65-78.

[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] Sukhatme, P.V. and Sukhatme, B.V. (1970) Sampling Theory of Surveys with Applications. Iowa State University Press, Ames.

[3] Cochran, W.G. (1977) Sampling Techniques. 3rd Edition, John Wiley & Sons, New York.

[4] Cochran, W.G. (1940) The Estimation of the Yields of the Cereal Experiments by Sampling for the Ratio of Grain to Total Produce. The Journal of Agricultural Science, 30, 262-275.

http://dx.doi.org/10.1017/S0021859600048012

[5] Robson, D.S. (1957) Application of Multivariate Polykays to the Theory of Unbiased Ratio-Type Estimation. Journal of the American Statistical Association, 52, 511-522.

http://dx.doi.org/10.1080/01621459.1957.10501407

[6] Murthy, M.N. (1964) Product Method of Estimation. Sankhya Series A, 26, 294-307.

[7] Singh, M.P. (1965) On the Estimation of Ratio and Product of the Population Parameters. Sankhya Series B, 27, 321-328.

[8] 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.

[9] Onyeka, A.C., Nlebedim, V.U. and Izunobi, C.H. (2014) A Class of Estimators for Population Ratio in Simple Random Sampling Using Variable Transformation. Open Journal of Statistics, 4, 284-291.

http://dx.doi.org/10.4236/ojs.2014.44029

[10] 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

[11] Singh, H.P. and Tailor, R. (2005) Estimation of Finite Population Mean Using Known Correlation Coefficient between Auxiliary Characters. Statistica, 4, 407-418.

[12] 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.

[13] 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.

[14] Onyeka, A.C. (2012) Estimation of Population Mean in Post-Stratified Sampling Using Known Value of Some Population Parameter(s). Statistics in Transition—New Series, 13, 65-78.