On the existence of best Mitscherlich, Verhulst, and West growth curves for generalized least-squares regression

摘要

Practical difficulties arise in fitting Mitscherlich, Verhulst, or West growth curves to data. Obstacles include divergent iterations, negative values for theoretically positive parameters, or the absence of any best-fitting curve. An analysis reveals that such obstacles occur near removable singularities of the objective function to be minimized for the regression. Such singularities lie at the transition to different types of curves, including exponentials, hyperbolae, lines, and step functions. Removing the singularities fits all such curves into a connected compactified topological space, which guarantees the existence of a global minimum for the continuous objective function, and which also provides a smooth and transparent transition from one type of curve to another.