Improved Ratio Estimators for Population Mean Based on Median Using Linear Combination of Population Mean and Median of an Auxiliary Variable (original) (raw)
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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.
2014
This manuscript deals with the estimation of population mean of the variable under study using an improved ratio type estimator utilizing the known values of median and coefficient of variation of auxiliary variable. The expressions for the bias and mean square error (MSE) of the proposed estimator are obtained up to the first order of approximation. The optimum estimator is also obtained for the optimum value of the constant of the estimator and its optimum properties are also studied. It is shown that the proposed estimator is better than the existing ratio estimators in the literature. For the justification of the improvement of the proposed estimator over others,
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.
An Improved Estimator of Population Mean using Information on Median of the Study Variable
International Journal of Mathematics Trends and Technology
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.
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.
In this paper, we proposed improved ratio estimators of Nasir's finite population mean using information of the linear combination of the values of tri-mean TM , quartile deviation QD and median d M of auxiliary variable. The bias and mean square errors (MSEs) of the proposed estimators have been obtained up to first order of approximation using Taylor's Series Expansion and the conditions for their efficiencies over some existing estimators have been established. The numerical illustration was also conducted to corroborate the theoretical results. The results of the empirical study show that the proposed estimators are more efficient than existing 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.
Efficient class of ratio cum median estimators for estimating the population median
PLOS ONE, 2023
In estimation theory, the use of auxiliary information significantly improves precision while estimating population parameters. In this paper, an efficient class of ratio cum median estimators of the population median is suggested using simple random sampling without replacement. The expressions for bias and mean square error of the proposed class are derived theoretically. The condition for the asymptotic optimum estimator is obtained with its bias and mean square error expressions. Under certain realistic conditions, the asymptotic optimum estimator is more proficient, based on analytical and numerical comparisons with some existing estimators that are members of the suggested class of estimators. The superiority of the proposed ratio cum median estimators is shown through real data applications. Such a new proposed estimator will be useful in the future for data analysis and making decisions.
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.
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.