On a generalized class of almost unbiased ratio estimators

Abstract

In sampling from finite populations to estimate the finite population mean/total of the study variable, one often observes available information on an associated auxiliary variable along with study variable to obtain an estimator, which is more efficient than the simple mean per unit estimator base d on observations on study variable only. The classical ratio estimator is one such estimator, which is simple to compute and is more efficient than the simple mean per unit estimator under certain conditions. However, the ratio estimator in spite of its simplicity is a biased estimator having bias of O⁢(1/n), n being the sample size. The bias may be negligible when the sample size is very large. For small sample size the bias may be substantially large so as to make the estimate unreliable to be used in practice. Beale (1962) and Tin (1965) have suggested some modified forms of ratio estimator which remove the first order bias, thus reducing the biases to O⁢(1/n2). Such modified ratio estimators are called Almost Unbiased Ratio estimators. This paper deals with construction of Generalized class of Almost unbiased ratio estimators using Srivastava’s (1971) generalized class of estimators and finds their expected values and variances in a generalized form. Further, as special cases Bahl-Tuteja’s (1991) ratio type exponential estimator and Swain’s (2014) square root transformation ratio type estimator are compared with regard to bias and efficiency along with numerical illustrations.