Mitscherlich's function is a well-known three-parameter non-linear regression function that quantifies the relation between a stimulus or a time variable and a response. Optimal designs for this function have been constructed only for normally distributed responses with homoscedastic variances. In this paper, we construct D-optimal designs for discrete and continuous responses having their distribution function in the exponential family. We also demonstrate the connection with D-optimality for weighted linear regression.

翻译：Micherlich 的函数是众所周知的三参数非线性回归函数,它量化了刺激或时间变量与响应之间的关系。该函数的最佳设计只针对通常分布的具有同性差异的响应而构建。在本文件中,我们为在指数式大家庭中具有分布功能的离散和连续响应构建了D-最佳设计。我们还展示了加权线性回归与D-最优化的关联。