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A Difference-Cum-Exponential Type Efficient Estimator of Population Mean
Published in Rakhee Kulshrestha, Chandra Shekhar, Madhu Jain, Srinivas R. Chakravarthy, Mathematical Modeling and Computation of Real-Time Problems, 2021
Kuldeep Kumar Tiwari, Sandeep Bhougal, Sunil Kumar
Precision is the reason for most of the research work in statistical theory and computation. Auxiliary information usually enhances the precision in survey sampling. It can be used at the selection stage or in estimation or on both. In the literature, auxiliary information is used by authors to construct various efficient estimators of different population parameters. The ratio estimator works better when there is a positive correlation between study and auxiliary variables, while the product estimator performs well in case of the negative correlation. Generally, a linear regression estimator is better than both ratio and product estimators. The equality in the efficiencies is obtained if the intercept of the regression line of y on x is zero. Since the regression estimator either performs better or equal to ratio and product estimators, it is convenient to use linear regression estimator than classical ratio and product estimator to gain in the efficiency. Many authors, such as [1–16], etc., worked on ratio and product type estimator to get the better results of such type estimator. Further, to get a better result, researchers worked on difference and exponential type estimators and showed its usefulness. Some of them are [17–20], etc.
Sampling strategies
Published in Andrew Metcalfe, David Green, Tony Greenfield, Mahayaudin Mansor, Andrew Smith, Jonathan Tuke, Statistics in Engineering, 2019
Andrew Metcalfe, David Green, Tony Greenfield, Mahayaudin Mansor, Andrew Smith, Jonathan Tuke
Ratio estimators and regression estimators: If the values of some covariate that is highly correlated with the variable of interest are known for the population then this information can be used to adjust sample estimates using regression, or in the case of proportionality a ratio estimator.
An EWMA control chart using two parametric ratio estimator
Published in Journal of Industrial and Production Engineering, 2018
Muhammad Noor-ul-Amin, Shahana Khan, Muhammad Aslam
Auxiliary information is obtained from a variable which is directly or inversely related to the variable of interest. Auxiliary information may be used at design stages or estimation stages. Many of the survey statisticians are utilizing auxiliary information at estimation stages to improve the efficiency of the estimation. The notion of auxiliary information is also used in control chart procedures to increase their performances. When study variable and auxiliary variable have a direct linear relationship, the ratio estimator is usually incorporated. For more information concerning auxiliary variable in sampling, readers can consult [8–12].