Abstract
This paper suggests some estimators for population mean of the study variable in simple random sampling and two-phase sampling using information on an auxiliary variable under second order approximation. Bahl and Tuteja (1991) and Singh et al. (2008) proposed some efficient estimators and studied the properties of the estimators to the first order of approximation. In this paper, we have tried to find out the second order biases and mean square errors of these estimators using information on auxiliary variable based on simple random sampling and two-phase sampling. Finally, an empirical study is carried out to judge the merits of the estimators over others under first and second order of approximation.
Highlights
Let U = (U1, U2, U3, . . . , UN) denote a finite population of distinct and identifiable units
For the estimation of population mean Y of a study variable Y, let us consider X to be the auxiliary variable that is correlated with study variable Y, taking the corresponding values of the units
Let a sample of size n be drawn from this population using simple random sampling without replacement (SRSWOR) and yi, xi (i = 1, 2, . . . , n) are the values of the study variable and auxiliary variable, respectively, for the ith units of the sample
Summary
Many authors including Singh and Tailor [1], Kadilar and Cingi [2], Singh et al [3], and Singh and Kumar [4] suggested estimators using some known population parameters of an auxiliary variable in simple random sampling. These authors studied the properties of the estimators to the first order of approximation. In this paper we have studied properties of some exponential estimators under second order of approximation in simple random sampling and two-phase sampling using information on an auxiliary variable
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