Some Generalised Ratio-Type Estimators

Abstract

Usual ratio estimator has limited utility in the sense that in populations where the condition P=Gy/Gx smaller than 1/a is not satisfied. It fails since in such as a case it becomes less efficient than the simple mean of the sample as an estimate of the population mean. In practice, we do come across many situations in which above condition is not satisfied. This condition generally requires the existences of a high correlation between the main and the auxiliary character. Sometimes an auxiliary character bears a high correlation with the main character but the information on it is either not available or involves a high cost for its collection. On the either hand, there may be some other auxiliary characters which are somewhat poorly correlated with the male character but information on them is either available or can be collected at a small cost. To deal with such situations, two modified ratio type estimators have been proposed. The biases and efficiencies for these estimators have been obtained and compared with that of simple mean. Usual ratio estimator and regression estimator. The use of these estimators has also been extended to the case of double sampling and to the case of negatively coo related characters. The case of sampling with varying probabilities to also discussed for the first estimator. Some empirical studies have also been conducted to investigate the various aspects of the proposed.