| In this thesis we study two statistical topics. Topic one deals with designs for 2-parameter generalized linear and nonlinear models. We suggest some methods based on T-systems and maximum principle to identify a class of models for which the D-optimal designs are precisely supported on 2 points. Furthermore, we utilize some geometric and analytical methods to obtain some efficient designs which are supported on more design points. These efficient designs can provide more opportunity for the model checking and prevent bias due to mis-specified initial parameters.; Topic two deals with the individual bioequivalence. We provide analytical solutions to the testing for individual bioequivalence. Through the comparison with the procedures proposed by the U.S. Food and Drug Administration, we recommend some procedures with high powers which control the type I error rates. These procedures can also provide meaningful interpretations to the individual bioequivalence. |
