Abstract—In recent years, new sampling techniques such as adaptive cluster sampling (ACS) have been developed. Since the theory of sample surveys plays an important role in the development of statistical science, different versions of ACS have been researched with different approaches. In this article, we also deal with the problem of estimating the mean of a hidden and rare clustered population utilizing auxiliary attribute information. Qualitative auxiliary data are significantly more accessible than quantitative auxiliary data in such populations. In this regard, we present two proposed classes of generalized regression-cum-exponential ratio type estimators under ACS with the transformed population approach. By the large sample approximation, we obtain mean square error of these two proposed classes of estimators using Taylor expansion. In addition to the calculations of theoretical comparisons and simulation studies, to investigate the optimal state of these two proposed classes in comparison with other existing estimators, we use experimental research among 179 countries of the world related to the estimation of the spread of the COVID- 19 disease in its early stages, which severity is clustered and hidden. The results indicate the very high desirability of these two proposed classes of estimators, especially for samples with small sizes based on the modified Horvitz–Thompson estimator. Such an accurate estimate of the number of new patients allows the health system to take appropriate countermeasures.

Keywords