D-Optimal Designs for the Mitscherlich Non-Linear Regression Function

Abstract: Mitscherlich’s function is a well-known three-parameter non-linearregression function that quantifies the relation between astimulus or a time variable and a response. It has manyapplications, in particular in the field of measurementreliability. Optimal designs for estimation of this function havebeen constructed only for normally distributed responses withhomoscedastic variances. In this paper we generalize thisliterature to D-optimal designs for discrete and continuousresponses having their distribution function in the exponentialfamily. We also demonstrate that our D-optimal designs can beidentical to and different from optimal designs for varianceweighted linear regression.