Abstract
In this paper, a class of double sampling difference cum ratio - type estimator using two auxiliary variables was proposed for estimating the finite population mean of the variable of interest. The expression for the bias and the mean square error of the proposed estimators are derived; in addition, some members of the class of the estimator are identified. The conditions under which the proposed estimators perform better than the sample mean and the existing double sampling ratio type estimators are derived. The empirical analysis showed that the proposed class of estimator performs better than the existing estimators considered in this study.
Highlights
Proper use of auxiliary variable is always known to improve the performance of estimators
Authors like Kadilar and Cingi, [1, 2], Raja et al, [3], Sisodia and Dwivedi, [4], Singh and Kakran, [5], Singh and Tailor, [6], Subramani and Kumarapandiyan, [7], Upadhyaya and Singh, [8] and Yan and Tian [10] have modified the classical ratio estimator by Cochran [10]using some known population parameters like coefficient of variation, coefficient of skewness e.t.c. , of an auxiliary variable when the population mean of the auxiliary variable is known
Sz2 are thesample variances of x and z respectively, sxy and sxz are the sample covariances between x and y and between x and z, respectively and H = 1, we have a member of the class of ratio-type regression estimator for estimating the population mean using two auxiliary variables when the population mean of two auxiliary variables are unknown presented below
Summary
Proper use of auxiliary variable is always known to improve the performance of estimators. Some authors like Kadilar and Cingi, [11], Mohanty, [12], Olkin, [13], Singh, [14] and Swain, [15], have worked on the use of two auxiliary variables in the estimation of the population mean of the variable interest. In real practical survey situation, the population means of the two auxiliary variables may not be available In this condition it is customary to use two phase sampling or double sampling scheme for estimating the population means of the auxiliary variables, see Cochran [10]. Suppose the population means of the auxiliary variables are unknown In such a situation we use a two phase sampling. Some known population parameters of one of the auxiliary variables were used to construct the estimator
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