Simulation study of small domain with calibration approach

Abstract

Some of the flexible models are available in the statistics literature are exponential and power distribution. They are very helpful in the modeling for situations when the shape and distribution of interested variables are positively skewed. We are presenting the calibration based estimates of domain total for exponential and the power model under such prevailing circumstances. Two different situations are considered: (i) domain total of the auxiliary variable is known and (ii) domain total of the auxiliary variable is unknown. To overcome the difficulties, to get calibration weights under second situation, two phase sampling technique is utilized. The Newton–Raphson method of approximation is used to estimate the Lagrange's multiplier. In addition, the efficiency of the proposed estimator has been given with support of the proposed weights under shortest Chi-square distance function. A numerical value based on the simulation study in terms of absolute relative bias and simulated relative standard error have been given using a real data of the Sweden municipality 1984 for comparison of the estimators. Finding shows that the proposed power function based calibration estimator is more efficient than the existing calibration based estimators of the domain total in both the situations. © 2022 John Wiley & Sons, Ltd.