D-optimal designs for modified exponential models with three parameters

Abstract

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.