SummaryThis paper presents a generalization of the logistic growth function based on a model for relative growth rates. The basic relative growth rate model is based on the Riccati differential equation, which has a solution that closely resembles the familiarS‐shaped logistic curve. For estimation purposes, a statistical version of this model is developed in which linear, exponential, and modified exponential growth in addition to logistic growth arise as special cases under various statistical hypotheses. The growth of yeast cells, population growth of the Netherlands and an example from the telephone industry are provided as illustrations of the mode