Estimation of a finite population total in varying probability sampling for multi-character surveys

The problems of estimating population total in multi-charter surveys are considered in a unified set up. Alternative estimators for Rao–Hartley–Cochran, Midzuno–Sen and other varying probability sampling schemes are proposed when the measure of size is not well related to the study variables. Some of the proposed estimators are found superior to the existing alternatives. A numerical study is carried out to investigate the performances of the proposed alternatives.