Calibration estimation of subpopulation total for direct and indirect situations

Sample surveys are conducted to estimate parameters of subpopulation such as mean, variance and totals, etc. The utility of the supporting information lies in the calibration technique, we use to estimate the subpopulation parameter. In this article, we propose calibration-based estimators for a total of the subpopulations. The defined estimators are based on gamma and exponential models. Since both models have right-skewed or positively skewed forms, the defined estimators are appropriate for right-skewed or positively skewed supportive variables. Two situations are considered in which the total of the supporting variable hold for all subpopulations: (i) the total of subpopulations of the supporting variable is known in advance and (ii) the total subpopulations of the supportive variable are not known. Due to difficulty arising in the calibration weight, we have carried out a simulation study in terms of absolute relative bias and simulated relative standard error using Sweden Municipalities 1984 (Sarndal, Swensson, and Wretman, 1992, Appendix B). A simulation study shows that the estimator based on the gamma function is more efficient than ratio, generalized regression, and exponential estimators for all subpopulations in the considered situations.