We introduce two adaptive allocation sampling designs. The introduced adaptive allocation sampling designs have some advantages over the previous adaptive allocations such as simplicity in conduction and independence of complicated calculations among strata. In Chapters 2 and 3, some biased estimators and a . In continuation of Chapter 5, we generalize the ratio and the regression estimator using Murthy's estimator in order to solve the problem of undefined ratio (and regression) estimator for a rare population. In Chapter 6, we also calculate the generalized ratio (and regression) estimator and variance estimator of the generalized ratio estimator when the general inverse sampling design is used. We also calculate the generalized ratio estimator and its estimate of variance for a combination of general inverse sampling design and adaptive clustered sampling design that is appropriate for a rare and clustered population. In another simulation study on a Blue-winged teal population that is rare and clustered we show the generalized ratio estimator for the combined sampling design is more efficient than that for conventional ratio estimator. In Chapter 6, we use the general inverse sampling design to modify all adaptive allocation sampling designs for a stratified rare population. The modification of adaptive allocations using the combined sampling design in a stratified rare and clustered population is applied similarly. Key Words: Adaptive allocation, Murthy's estimator, Optimum allocation, Optimum stratification, Rare population, Ratio estimator, and Regression estimator.