An Improved Estimator of Population Mean using Information on Median of the Study Variable (original) (raw)
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An Improved Estimator of Population Mean using Information on Median of the Study Variable 1
The present paper advocates the estimation of population mean of the study variable by utilizing the information on median of the study variable. A generalized ratio type estimator has been proposed for this purpose. The expressions for the bias and mean squared error of the proposed estimator have been derived up to the first order of approximation. The optimum value of the characterizing scalar has also been obtained. The minimum value of the proposed estimator for this optimum value of the characterizing scalar is obtained. A theoretical efficiency comparison of the proposed estimator has been made with the mean per unit estimator, usual ratio of Cochran (1940) and usual regression estimator of Watson (1937),Bahl and Tuteja (1991)estimator, Kadilar (2016) and Subramani (2016) estimators. Theoretical results are supported by the numerical illustration and foundthat proposed estimatorperforms better than theexisting estimators.
ESTIMATING POPULATION MEAN USING KNOWN MEDIAN OF THE STUDY VARIABLE
This present paper concerns with the estimation of population mean of the study variable by utilizing the known median of the study variable. A generalized ratio type estimator has been proposed for this purpose. The expressions for the bias and mean squared error of the proposed estimator have been derived up to the first order of approximation. The optimum value of the characterizing scalar has also been obtained. The minimum value of the proposed estimator for this optimum value of the characterizing scalar is obtained. A theoretical efficiency comparison of the proposed estimator has been madewith the mean per unit estimator, usual ratio estimator of Cochran (1940), usual regression estimator of Watson (1937),Bahl and Tuteja (1991), Kadilar (2016) and Subramani (2016) estimators. Through the numerical study, the theoretical findings are validated and it has been found that proposed estimate or performs better than the existing estimators.
AN EFFICIENT ESTIMATOR FOR ESTIMATING FINITEPOPULATION MEAN USING KNOWN MEDIAN OF THE STUDY VARIABLE
The present paper concerns with the estimation of population mean of the study variable by utilizing the known median of the study variable. A generalized ratio type estimator has been proposed for this purpose. The expressions for the bias and mean squared error of the proposed estimator have been derived up to the first order of approximation. The optimum value of the characterizing scalar has also been obtained. The minimum value of the proposed estimator for this optimum value of the characterizing scalar is obtained. A theoretical efficiency comparison of the proposed estimator has been made with the mean per unit estimator, usual ratioestimator of Cochran (1940), usual regression estimator of Watson (1937) ,Bahl and Tuteja estimator (1991), Kadilar (2016) and Subramani (2016) estimators. Through the numerical study, the theoretical findings are validated and it has been found that proposed estimatorperforms better than theexisting estimators.
Pakistan Journal of Statistics and Operation Research, 2013
The present paper deals with a modified ratio estimator for estimation of population mean of the study variable when the population median of the auxiliary variable is known. The bias and mean squared error of the proposed estimator are derived and are compared with that of existing modified ratio estimators for certain known populations. Further we have also derived the conditions for which the proposed estimator performs better than the existing modified ratio estimators. From the numerical study it is also observed that the proposed modified ratio estimator performs better than the existing modified ratio estimators for certain known populations.
This present paper concerns with the estimation of population mean of the study variable by utilizing the known median of the study variable. A generalized ratio type estimator has been proposed for this purpose. The expressions for the bias and mean squared error of the proposed estimator have been derived up to the first order of approximation. The optimum value of the characterizing scalar has also been obtained. The minimum value of the proposed estimator for this optimum value of the characterizing scalar is obtained. A theoretical efficiency comparison of the proposed estimator has been madewith the mean per unit estimator, usual ratio estimator of Cochran (1940), usual regression estimator of Watson (1937),Bahl and Tuteja (1991), Kadilar (2016) and Subramani (2016) estimators. Through the numerical study, the theoretical findings are validated and it has been found that proposed estimate or performs better than the existing estimators.
American Journal of Operational Research, 2014
In this manuscript the two efficient estimators of population mean using linear combination of population mean and median of auxiliary variable have been proposed. The expressions for the bias and mean square error (MSE) have been obtained up to the first order of approximation. A comparison has been made with the mentioned existing estimators of population mean. A numerical study has also been carried out to justify the improvement of the proposed estimators over other mentioned estimators of population mean of study variable.
Pakistan Journal of Statistics and Operation Research, 2013
The present paper deals with a modified ratio estimator for estimation of population mean of the study variable when the population median of the auxiliary variable is known. The bias and mean squared error of the proposed estimator are derived and are compared with that of existing modified ratio estimators for certain known populations. Further we have also derived the conditions for which the proposed estimator performs better than the existing modified ratio estimators. From the numerical study it is also observed that the proposed modified ratio estimator performs better than the existing modified ratio estimators for certain known populations.
The present paper concerns with the estimation of population mean of the study variable by utilizing the known median of the study variable. A generalized ratio type estimator has been proposed for this purpose. The expressions for the bias and mean squared error of the proposed estimator have been derived up to the first order of approximation. The optimum value of the characterizing scalar has also been obtained. The minimum value of the proposed estimator for this optimum value of the characterizing scalar is obtained. A theoretical efficiency comparison of the proposed estimator has been made with the mean per unit estimator, usual ratioestimator of Cochran (1940), usual regression estimator of Watson (1937) ,Bahl and Tuteja estimator (1991), Kadilar (2016) and Subramani (2016) estimators. Through the numerical study, the theoretical findings are validated and it has been found that proposed estimatorperforms better than theexisting estimators.
Hacettepe Journal of Mathematics and Statistics, 2016
This paper deals with ecient ratio type estimators for estimatingnite population mean under simple random sampling scheme by using the knowledge of known median of a study and an auxiliary variable. Expressions for the bias and mean squared error of the proposed ratio type estimators are derived up to rst order of approximation. It is found that our proposed estimators perform better as compared to the traditional ratio estimator, regression estimator, Subramani and Kumarapandiyan [23], Subramani and Prabavathy [24] and Yadav et al. [28] estimators. In addition, theoretical ndings are veried with the help of real data sets.
An Estimator of the Mean Estimation of Study Variable Using Median of Auxiliary Variable
In the present study, I propose a modified estimator for estimating the population mean of the study variable auxiliary information when the population mean and the population median of the auxiliary variable is known. The expression of bias and mean squared error (MSE) of the proposed estimator is derived. Some existing estimators are also discussed. Comparisons of the proposed estimator with the other estimators are carried out. The results obtained are illustrated numerically by using three natural populations considered in the literature.