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Estimation of Population Ratio in Post-Stratified Sampling Using Variable Transformation
Department of Statistics, Federal University of Technology, Owerri, Nigeria
Department of Statistics, Federal University of Technology, Owerri, Nigeria
Department of Statistics, Federal University of Technology, Owerri, Nigeria
- 1 Department of Statistics, Federal University of Technology, Owerri, Nigeria
- 2 Department of Statistics, Federal University of Technology, Owerri, Nigeria
- 3 Department of Statistics, Federal University of Technology, Owerri, Nigeria
Open Journal of Statistics·Volume 05 (2015)·Pages 1–9·Published 20 January 2015·DOI10.4236/ojs.2015.51001
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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.
KeywordsVariable TransformationCombined-Type EstimatorRatioProduct and Regression-Type EstimatorsMean Squared Error
- 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.
- Sukhatme, P.V. and Sukhatme, B.V. (1970) Sampling Theory of Surveys with Applications. Iowa State University Press, Ames.
- Cochran, W.G. (1977) Sampling Techniques. 3rd Edition, John Wiley & Sons, New York.
- 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
- 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
- Murthy, M.N. (1964) Product Method of Estimation. Sankhya Series A, 26, 294-307.
- Singh, M.P. (1965) On the Estimation of Ratio and Product of the Population Parameters. Sankhya Series B, 27, 321-328.
- 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.
- 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
- 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
- Singh, H.P. and Tailor, R. (2005) Estimation of Finite Population Mean Using Known Correlation Coefficient between Auxiliary Characters. Statistica, 4, 407-418.
- 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.
- 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.
- 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.