IMPROVED ESTIMATION OF FINITE POPULATION VARIANCE USING QUARTILES

Authors : Housila P SİNGH, Surya Kant PAL, Ramkrishna S SOLANKİ

Pages : 116-121

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Publication Date : 2013-12-31

Article Type : Research Paper

Abstract :We have addressed the problem of estimation of finite population variance using known values of quartiles of an auxiliary variable. Some ratio type estimators have been proposed with their properties in simple random sampling. The suggested estimators have been compared with the usual unbiased and ratio estimators. In addition, an empirical study is also provided in support of theoretical findings.Variation is present everywhere in our day to day life. It is law of nature that no two things or individuals are exactly alike. For instance, a physician needs a full understanding of variation in the degree of human blood pressure, body temperature and pulse rate for adequate prescription. A manufacture needs constant knowledge of the level of variation in peoples reaction to his product to be able to known whether to reduce or increase his price, or improve the quality of his product. An agriculturist needs an adequate understanding of variations in climate factors especially from place to place insert ignore into journalissuearticles values(or time to time); to be able to plan on when, how and where to plant his crop. Many more situations can be encountered in practice where the estimation of population variance of the study variable y assumes importance. In survey sampling, known auxiliary information is often used at the estimation stage to increase the precision of the estimators of population variance. For these reasons various authors such as Singh and Solanki insert ignore into journalissuearticles values(2009-2010);, Tailor and Sharma insert ignore into journalissuearticles values(2012);, Solanki and Singh insert ignore into journalissuearticles values(2013);, Singh and Solanki insert ignore into journalissuearticles values(2013a, b);, Subramani and Kumarapandiyan insert ignore into journalissuearticles values(2013a, b); and Yadav and Kadilar insert ignore into journalissuearticles values(2013a, b); have paid their attention towards the improved estimator of population variance of the study variable y using information on the known parameters of the auxiliary variable x such as mean, variance, coefficient of skewness, coefficient of kurtosis, correlation coefficient between the study variable y and the auxiliary variable x etc. Recently Subramani and Kumarapandiyan insert ignore into journalissuearticles values(2012a, b); have considered the problem of estimating the population variance of study variable y using information on variance, quartiles, inter-quartile range, semi-quartile range and semi-quartile average of the auxiliary variable x. In this paper our quest is to estimate the unknown population variance of study variable y by improving the estimators suggested by Subramani and Kumarapandiyan insert ignore into journalissuearticles values(2012a, b); using same information on an auxiliary variable x. Let U = insert ignore into journalissuearticles values(U1, U2,..., UN ); be finite population of size N and insert ignore into journalissuearticles values(y, x); are insert ignore into journalissuearticles values(study, auxiliary); variables taking values insert ignore into journalissuearticles values(yi , xi); respectively for the i-th unit Ui of the finite population U. Let a simple random sample insert ignore into journalissuearticles values(SRS); of size n be drawn without replacement insert ignore into journalissuearticles values(WOR); from the finite population U. The usual unbiased estimator s 2 y and the estimators of the population variance due to Isaki insert ignore into journalissuearticles values(1983); and Subramani and Kumarapandiyan insert ignore into journalissuearticles values(2012a, b); are given in the Table 1 along with their biases and mean squared errors insert ignore into journalissuearticles values(MSEs);.
Keywords : Study variable, Auxiliary variable, Bias, Mean squared error, Quartiles, Simple random sampling