A modified ratio-product estimator of population mean using some known parameters of the auxiliary variable (original) (raw)
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Bayero Journal of Pure and Applied Sciences, 2017
For the past decades, the estimation of population mean is one of sampling survey techniques and much effort has been employed to improve the precision of estimates. In this research work, we proposed a modified ratio mean of the variable of interest using median stratified random sampling scheme. The expression of bias and MSE of the proposed estimator have been obtained under large sample approximation, asymptotically optimum estimator (AOE) is identified with its approximate MSE formula. Estimator based on "estimated optimum values" was also investigated. Theoretical and empirical comparison of proposed estimator with some other ratio and product estimator justified the performance of the proposed estimat minimum of 15 percent reduction in the MSE from each of the existing ratio and product estimators considered. Thus most preferred over the existing estimators for the use in practical application.
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.
Modified Ratio-Cum-Product Estimators of Population Mean Using Two Auxiliary Variables
Asian Journal of Research in Computer Science, 2020
A percentile is one of the measures of location used by statisticians showing the value below which a given percentage of observations in a group of observations fall. A family of ratio-cum-product estimators for estimating the finite population mean of the study variable when the finite population mean of two auxiliary variables are known in simple random sampling without replacement (SRSWOR) have been proposed. The main purpose of this study is to develop new ratio-cum-product estimators in order to improve the precision of estimation of population mean in sample random sampling without replacement using information of percentiles with two auxiliary variables. The expressions of the bias and mean square error (MSE) of the proposed estimators were derived by Taylor series method up to first degree of approximation. The efficiency conditions under which the proposed ratio-cum-product estimators are better than sample man, ratio estimator, product estimator and other estimators considered in this study have been established. The numerical and empirical results show that the proposed estimators are more efficient than the sample mean, ratio estimator, product estimator and other existing estimators. Original Research Article Muili et al.; AJRCOS, 6(1): 55-65, 2020; Article no.AJRCOS.59248 56
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.
Oriental Journal of Physical Sciences, 2023
Some existing estimators based on auxiliary attribute have been proposed by many authors. In this paper, we use the concept of power transformation to modify some existing estimators in order to obtain estimators that are applicable when there is positive or negative correlation between the study and auxiliary variable. The properties (Biases and MSEs) of the proposed estimators were derived up to the first order of approximation using Taylor series approach. The efficiency comparison of the proposed estimators over some existing estimators considered in the study were established. The empirical studies were conducted using existing population parameters to investigate the proficiency of the proposed estimators over some existing estimators. The results revealed that the proposed estimators have minimum Mean Square Errors and higher Percentage Relative Efficiencies than the conventional and other competing estimators in the study. These implies that the proposed estimators are more efficient and can produce better estimates of the population mean compared to the existing estimators considered in the study.