Mixture Regression-Cum-Ratio Estimator Using Multi-Auxiliary Variables and Attributes in Single-Phase Sampling

In this paper, we have proposed a class of mixture regression-cum-ratio estimator for estimating population mean by using information on multiple auxiliary variables and attributes simultaneously in single-phase sampling and analyzed the properties of the estimator. An empirical was carried out to compare the performance of the proposed estimator with the existing estimators of finite population mean using simulated population. It was found that the mixture regression-cum-ratio estimator was more efficient than ratio and regression estimators using one auxiliary variable and attribute, ratio and regression estimators using multiple auxiliary variables and attributes and regression-cum-ratio estimators using multiple auxiliary variables and attributes in single-phase sampling for finite population.

Cite this paper

Mutembei, T. , Kung’u, J. and Ouma, C. (2014) Mixture Regression-Cum-Ratio Estimator Using Multi-Auxiliary Variables and Attributes in Single-Phase Sampling. Open Journal of Statistics, 4, 367-376. doi: 10.4236/ojs.2014.45036.

Conflicts of Interest

The authors declare no conflicts of interest.

 [1] Neyman, J. (1938) Contribution to the Theory of Sampling Human Populations. Journal of the American Statistical Association, 33, 101-116. http://dx.doi.org/10.1080/01621459.1938.10503378 [2] Watson, D.J. (1937) The Estimation of Leaf Areas. Journal of the Agricultural Science, 27, 474-504.http://dx.doi.org/10.1017/S002185960005173X [3] Cochran, W.G. (1940) The Estimation of the Yields of the Cereal Experiments by Sampling for the Ratio of Grain to Total Produce. Journal of the Agricultural Science, 30, 262-275. http://dx.doi.org/10.1017/S0021859600048012 [4] Hansen, M.H. and Hurwitz, W.N. (1943) On the Theory of Sampling from Finite Populations. Annals of Mathematical Statistics, 14, 333-362. http://dx.doi.org/10.1214/aoms/1177731356 [5] Olikin, I. (1958) Multivariate Ratio Estimation for Finite Population. Biometrika, 45, 154-165.http://dx.doi.org/10.1093/biomet/45.1-2.154 [6] Shukla, G.K. (1965) Multivariate Regression Estimate. Journal of the Indian Statistical Association, 3, 202-211. [7] Raj, D. (1965) On a Method of Using Multi-Auxiliary Information in Sample Surveys. Journals of the American Statistical Association, 60, 154-165. http://dx.doi.org/10.1080/01621459.1965.10480789 [8] Singh, M.P. (1967) Ratio-Cum-Product Method of Estimation. Metrika, 12, 34-42. http://dx.doi.org/10.1007/BF02613481 [9] Jhajj, H.S., Sharma, M.K. and Grover, L.K (2006) A Family of Estimator of Population Mean Using Information on Auxiliary Attributes. Pakistan Journal of Statistics, 22, 43-50. [10] Rajesh, S., Pankaj, C., Nirmala, S. and Florentins, S. (2007) Ratio-Product Type Exponential Estimator for Estimating Finite Population Mean Using Information on Auxiliary Attributes. Renaissance High Press, USA. [11] Naik, V.D. and Gupta, P.C. (1996) A Note on Estimation of Mean with Known Population of Auxiliary Character. Journal of the Indian Society of Agricultural Statistics, 48, 151-158. [12] Bahl, S. and Tuteja, R.K. (1991) Ratio and Product Type Estimator. Information and Optimization Science, 12, 159-163. http://dx.doi.org/10.1080/02522667.1991.10699058 [13] Hanif, M., Haq, I.U. and Shahbaz, M.Q. (2009) On a New Family of Estimator Using Multiple Auxiliary Attributes. World Applied Science Journal, 11, 1419-1422. [14] Hanif, M., Haq, I. and Shahbaz, M.Q. (2010) Ratio Estimators Using Multiple Auxiliary Attributes. World Applied Sciences Journal, 8, 133-136. [15] Robson, D.S. (1952) Multiple Sampling of Attributes. Journal of the American Statistical Association, 47, 203-215.http://dx.doi.org/10.1080/01621459.1952.10501164 [16] Samiuddin, M. and Hanif, M. (2007) Estimation of Population Mean in Single and Two-Phase Sampling with or without Additional Information. Pakistan Journal of Statistics, 23, 99-118. [17] Ahmad, Z. (2008) Generalized Multivariate Ratio and Regression Estimators for Multi-Phase Sampling. Ph.D. Thesis, National College of Business Administration and Economics, Lahore. [18] Zahoor, A., Muhhamad, H. and Munir, A. (2009) Generalized Regression-Cum-Ratio Estimators for Two-Phase Sampling Using Multiple Auxiliary Variables. Pakistan Journal of Statistics, 25, 93. [19] Kung’u, J. and Odongo, L. (2014) Ratio-Cum-Product Estimator Using Multiple Auxiliary Attributes in Single Phase Sampling. Open Journal of Statistics, 4, 239-245. http://dx.doi.org/10.4236/ojs.2014.44023 [20] Kung’u, J. and Odongo, L. (2014) Ratio-Cum-Product Estimator Using Multiple Auxiliary Attributes in Two-Phase Sampling. Open Journal of Statistics, 4, 246-257. http://dx.doi.org/10.4236/ojs.2014.44024 [21] Moeen, M., Shahbaz, Q. and HanIf, M. (2012) Mixture Ratio and Regression Estimators Using Multi-Auxiliary Variable and Attributes in Single Phase Sampling. World Applied Sciences Journal, 18, 1518-1526. [22] Arora, S. and Bansi, L. (1989) New Mathematical Statistics. Satya Prakashan, New Delhi.