Abstract
In this paper, a generalized class of estimators for the estimation of population median are proposed under simple random sampling without replacement (SRSWOR) through robust measures of the auxiliary variable. Three robust measures, decile mean, Hodges–Lehmann estimator, and trimean of an auxiliary variable, are used. Mathematical properties of the proposed estimators such as bias, mean squared error (MSE), and minimum MSE are derived up to first order of approximation. We considered various real-life datasets and a simulation study to check the potentiality of the proposed estimators over the competitors. Robustness is also examined through a real dataset. Based on the fascinating results, the researchers are encouraged to use the proposed estimators for population median under SRSWOR.
Highlights
Extensive work has been done on the estimation of the population mean, proportion, variance, regression coefficient, and so forth; but very little attention has been made to propose the efficient estimators of the median
After Kuk and Mak’s [4] estimator, Singh et al [5], Aladag and Cingi [6], Solanki and Singh [7], Shabbir and Gupta [8], Baig et al [9], and Shabbir et al [10] have developed different estimators for estimating finite population median based on the known conventional measures of the auxiliary variable under different sampling schemes
We proposed the generalized classes of estimators for estimating population median under simple random sampling using robust measures of an auxiliary variable
Summary
Extensive work has been done on the estimation of the population mean, proportion, variance, regression coefficient, and so forth; but very little attention has been made to propose the efficient estimators of the median. Let MY and MX be the population median of the study and auxiliary variables with the probability density functions given by fY(MY) and fX(MX), respectively. The problem under consideration is to estimate the median for finite population and suggest some generalized classes of estimators by utilizing known robust measures of an auxiliary variable under SRSWOR. We discuss the usual and well-known estimators for estimating population median under SRSWOR as suggested by different authors. Kuk and Mak [4] suggested a ratio-type estimator by assuming the known median of the X variable. Where d7 and d8 are unknown constants whose values need to be determined, a and b are the known population parameters, and α1, α2 and c are the scalar quantities
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