Product and exponential product estimators in adaptive cluster sampling under different population situations

In this paper,the product and exponential product estimators have been proposed for estimating the population mean using population mean of an auxiliary variable,when there is negative correlation between the variables,under adaptive cluster sampling (acs) design. the expressions for mean squared error (mse) and bias of the proposed estimators have been derived. two simulated populations are used and simulation studies have been conceded out to reveal and match the efficiencies of the estimators. the proposed estimators have been matched with conventional estimators and estimators in acs. the simulation results showed that the proposed product and exponential product estimators are more efficient as compare to conventional as well as hansen-hurwitz and ratio estimators in acs. © pakistan academy of sciences.