Tatik Widiharih

Algorithms of D-optimal designs for Morgan Mercer Flodin (MMF) models with three parameters

Morgan Mercer Flodin (MMF) model is used in many areas including biological growth studies, animal and husbandry, chemistry, finance, pharmacokinetics and pharmacodynamics. Locally D-optimal designs for Morgan Mercer Flodin (MMF) models with three parameters are investigated. We used the Generalized Equivalence Theorem of Kiefer and Wolvowitz to determine D-optimality criteria. Number of roots for standardized variance are determined using Tchebysheff system concept and it is used to decide that the design is minimally supported design. In these models, designs are minimally supported designs with uniform weight on its support, and the upper bound of the design region is a support point.

D-optimal designs for modified exponential models with three parameters

Locally D-optimal designs for modified exponential models with three parameters and homoscedastic error are investigated. D-optimal criteria is based on Equivalence Theorem of Kiefer Wolfowitz [19]. Determination whether the design that meets the specified model is minimally supported design is based on Theorem 1 of Li and Majumdar [21] which examines the behavior of the standardized variance function in a vertical neighborhood of zero. Tchebychev system and their properties plays a critical role on it. The results show that the designs are minimally supported and the design points are interior points of the design region in the interval [0, b], where b is selected such that the curve is relatively constant and closed to 0. At several design regions, which are the subsets of interval [0, b], design points have a specific pattern.