Publication:

Chain ratio and product estimators for population mode using two-phase sampling scheme

Background For skewed datasets, the mode is utilized as a more appropriate measure of location. We formed chain ratio and product estimators for the population mode using two types of auxiliary information under the two-phase sampling scheme.

Methods Expressions for biases and mean square errors for the formed estimators up to the first order of approximation are obtained. The confidence intervals of the estimators are obtained and the aspects related to fixed cost and fixed variance are also studied. A simulation study is performed to support the theoretical outcomes. A real dataset is also provided which was collected from the department of agriculture, United States.

Results The simulation results for the fixed first-phase sample size  and the second-phase sample size  show that the mean square error is 0.035, the bias is 0.012, the confidence interval is 2.67-3.15, and the cost of the survey under the fixed variance is ₹ 194.67 of the proposed estimator , which is lower than 0.039, 0.055, 2.70-3.20, and ₹ 247.37 of the ratio estimator  and 0.078, 0.041, 2.57-3.31, and ₹ 268.73 of the naive estimator .

Conclusions The simulation results show that the proposed estimator  performs better than the ratio estimator  and the naive estimator .