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.

在这项工作中，考虑了可用于描述各种数据类型的灵活的非正态分布类的未知参数估计的最佳设计问题。可以将称为单纯形色散模型的特定模型应用于限制在（0，1）区间内的比例（或成分）结果模型。这里的主要兴趣是确定最佳实验设置，以便能够更准确，更有效地估计未知模型参数。在本地$d$通过相应的等价定理，对用于单纯形色散模型中参数的准确估计的最佳设计进行了描述，并在某些情况下利用一些给定的先验信息，给出了最佳设计结果以供说明。使用包括水净化实验和剂量研究在内的示例来证明相应的功效$d$-最佳设计。