A Ratio-cum-Dual to Ratio Estimator of Population Variance Using Qualitative Auxiliary Information Under Simple Random Sampling
In this paper we have proposed a class of ratio-cum-dual to ratio estimators for estimating population variance of the variable under study, using known values of some population parameters of auxiliary variable, which is available in the form of an attribute. The expressions for the bias and mean squared error of the proposed estimators have been derived up to the first order of approximation. A comparison has been made with some well-known estimators of population variance available in the literature when auxiliary information is in qualitative form. It has been shown that the proposed estimator is better than the existing estimators under the optimum condition. For illustration, an empirical study has been carried out.
Cochran, W.G., 1977. Sampling Techniques. New-York, John Wiley and Sons. Isaki, C.T. (1983): Variance estimation using auxiliary information. Jour. Amer. Stat. Assoc., 78, 117-123. http://dx.doi.org/10.1080/01621459.1983.10477939
Jhajj, H. S. Sharma, M. K. and Grover, L. K. (2006) A family of estimators of population mean using the information on an auxiliary attribute. Pak. J. Statist., 22 (1), 43-50.
Kadilar, C. and Cingi, H. (2006): Ratio estimators for the population variance in simple and stratified random sampling. Applied Mathematics and Computation, 173, 1047-1059. http://dx.doi.org/10.1016/j.amc.2005.04.032
Misra, S. and Yadav, S.K. (2010): Ratio type estimator of population variance using qualitative auxiliary information. International transactions in mathematical sciences and computers, Vol. 3, 2, 313-322.
Mukhopadhyay, P., 1998. Theory and methods of survey sampling, Prentice Hall of India private limited, New Delhi, India.
Singh, H.P., Upadhyaya, L.N. and Namjoshi, U.D. (1988). Estimation of finite population variance. Curr. Sc. 57:1331-1334.
Singh, S. (2003). Advanced sampling theory with applications. Kluwer Academic. Press. http://dx.doi.org/10.1007/978-94-007-0789-4
Sukhatme, P.V., and Sukhatme, B.V. 1970. Sampling theory of surveys with applications. Asia Publishing House, New Delhi.
Shabbir, J. and Gupta, S. On estimating the finite population means with known population proportion of an auxiliary variable, Pak. J. Statist., 23(1), 1-9, 2007.
Sharma, B. and Tailor, R. A New Ratio-Cum-Dual to Ratio Estimator of Finite Population Mean in Simple Random Sampling, Global Journal of Science Frontier Research, Vol. 10, 1, 27-31, 2010.
Upadhyaya, L.N. and Singh, H.P. 2001. Estimation of the population standard deviation using information. Am. Jour. Math. Manag. Sci. 21:345-358