2018Journal of King Saud University - ScienceOpen access

Enhanced estimation of population mean in the presence of auxiliary information

Muhammad Irfan, Maria Javed, Zhengyan Lin

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Abstract

In this article, we propose a general family of exponential-type estimators for enhanced estimation of population mean in simple random sampling. These estimators are based on the available parameters of the auxiliary variable such as coefficient of skewness, coefficient of kurtosis, standard deviation and coefficient of variation etc. Expressions for bias, mean squared error and minimum mean squared error of the proposed family are derived up to first degree of approximation. Five natural populations are considered to assess the performance of the proposed estimators. Numerical findings confirm that the proposed estimators dominate over the existing estimators such as sample mean, ratio, regression, Singh et al. (2008, 2009), Upadhyaya et al. (2011), Yadav and Kadilar (2013) and Kadilar (2016) in terms of mean squared error.

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What this paper is about

In this article, we propose a general family of exponential-type estimators for enhanced estimation of population mean in simple random sampling. These estimators are based on the available parameters of the auxiliary variable such as coefficient of skewness, coefficient of kurtosis, standard deviation and coefficient of variation etc. Expressions for bias, mean squared error and minimum mean squared error of the proposed family are derived up to first degree of approximation. Five natural populations are considered to assess the performance of the proposed estimators. Numerical findings confirm that the proposed estimators dominate over the existing estimators such as sample mean, ratio, regression, Singh et al. (2008, 2009), Upadhyaya et al. (2011), Yadav and Kadilar (2013) and Kadilar (2016) in terms of mean squared error.

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Available abstract

In this article, we propose a general family of exponential-type estimators for enhanced estimation of population mean in simple random sampling. These estimators are based on the available parameters of the auxiliary variable such as coefficient of skewness, coefficient of kurtosis, standard deviation and coefficient of variation etc. Expressions for bias, mean squared error and minimum mean squared error of the proposed family are derived up to first degree of approximation. Five natural populations are considered to assess the performance of the proposed estimators. Numerical findings confirm that the proposed estimators dominate over the existing estimators such as sample mean, ratio, regression, Singh et al. (2008, 2009), Upadhyaya et al. (2011), Yadav and Kadilar (2013) and Kadilar (2016) in terms of mean squared error.

Key concepts: Estimator, Kurtosis, Mathematics, Mean squared error, Statistics, Population mean, Standard deviation, Skewness

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