Estimation of finite population mean in simple random sampling and stratified random sampling using two auxiliary variables

In this paper, we propose a generalized class of exponential type estimators for estimating the finite population mean using two auxiliary attributes under simple random sampling and stratified random sampling. The bias and mean squared error (MSE) of the proposed class of estimators are derived up to first order of approximation. Both empirical study and theoretical comparisons are discussed. Four populations are used to support the theoretical findings. It is observed that the proposed class of estimators perform better as compared to all other considered estimator in simple and stratified random sampling.

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Efficient Estimator of a Finite Population Mean Using Two Auxiliary Variables and Numerical Application in Agricultural, Biomedical, and Power Engineering

Mathematical Problems in Engineering ◽

10.1155/2017/8704734 ◽

2017 ◽

Vol 2017 ◽

pp. 1-7 ◽

Cited By ~ 1

Author(s):

Jingli Lu

Keyword(s):

Random Sampling ◽

Finite Population ◽

Simple Random Sampling ◽

Power Engineering ◽

Comparison Study ◽

Auxiliary Variables ◽

Numerical Application ◽

Population Mean ◽

Theoretical Results ◽

Better Than

To improve the efficiency of an estimator with two auxiliary variables, we propose a new estimator of a finite population mean under simple random sampling. The bias and mean square error expressions of the proposed estimator have been obtained. In a comparison study, we found that the new estimator was consistently better than those of Abu-Dayyeh et al., Kadilar and Cingi, and Malik and Singh, as well as the regression estimator using two auxiliary variables, and that the minimum MSE values of the previous three above reported estimators were equal. We used four numerical examples in agricultural, biomedical, and power engineering to support these theoretical results, thus enriching the theory of survey samples by the development of new estimators with two auxiliary variables.

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Modified Ratio-Cum-Product Estimators of Population Mean Using Two Auxiliary Variables

Asian Journal of Research in Computer Science ◽

10.9734/ajrcos/2020/v6i130152 ◽

2020 ◽

pp. 55-65

Author(s):

J. O. Muili ◽

E. N. Agwamba ◽

Y. A. Erinola ◽

M. A. Yunusa ◽

A. Audu ◽

...

Keyword(s):

Random Sampling ◽

Finite Population ◽

Simple Random Sampling ◽

Degree Of Approximation ◽

Ratio Estimator ◽

Auxiliary Variables ◽

Sampling Without Replacement ◽

Sample Mean ◽

Population Mean ◽

Product Estimator

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.

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