D-optimal designs for estimation of parameters in a simplex dispersion model with proportional data

In this work, optimal design problems for estimation of unknown parameters for a flexible class of non-normal distributions useful for describing various data types are considered. A particular model, designated the simplex dispersion model, can be applied to model proportional (or compositional) outcomes confined within the (0, 1) interval. The main interest here is to determine the optimal experimental settings to be able to estimate the unknown model parameters more accurately and efficiently. Locally D -optimal designs for accurate estimation of parameters in the simplex dispersion model are characterized through the corresponding equivalence theorem and under certain cases with some given prior information, optimal design results are presented for illustration. Examples including a water purification experiment and a dose study are used to demonstrate the efficiencies of the corresponding D -optimal designs.