Tchebycheff system and its application to construct the minimally supported design for generalized exponential model

Abstract

Abstract The generalized exponential model has a unimodal curve shape, so it can be used as a growth function model. Determination of the supported designs must be run to construct the model is a serious problem. Based on the supported designs are expected to meet the optimal criteria. In this paper, we use the D-optimal criteria, which is minimized the variance of the parameter estimator. The standardized variance function has an important role in the D-optimal design. The D-optimal design is a design with the value of standardized variance at supported designs is equal to the number of parameters. The number of roots of the standardized variance function needs to be find to determine the number of supported designs. Tchebycheff system is a set of continuous functions that can be used to determine the number of roots of a function. A design with the number of supported designs same as the number of roots of the standardized variance function with uniform weight is a minimally supported design.