This paper addresses the problem of estimating ratio of two population means by using quantitative auxiliary knowledge in the form of first and second moments. Through this paper, an improved generalized two phase sampling estimator has been proposed. The relative bias and mean squared error of the suggested estimator has been derived and studied. Also, a comparative study with the conventional estimators has been included to establish its superiority. Besides theoretical comparisons, a subset of optimum estimators having the same minimum mean squared error (MSE) is also explored. An empirical study is also carried out to support theoretical results.

Through this paper, we suggest an enhanced two-phase sampling ratio type estimator for the efficient estimation of population parameter mean by utilizing known values of moments of an auxiliary variable. The salient features affiliated with the developed estimator characterized by mean squared error and bias is also assessed. In addition, the expression for minimum mean squared error for the optimum values has been obtained. To establish the superiority of suggested estimator, efficiency comparison with some existing estimators has been accomplished. An empirical study to elucidate theoretical results through two real population data sets is also presented as an illustration.

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