The Fitting of a Generalization of the Logistic Curve

Special cases were originally proposed by Putter [1920] for various types of animal growth (see e.g. von Bertalanffy [1957]), and recently Richards [1959] has exemplified the general form of the curves and suggested that they may be useful for the empirical description of plant growth. For further details of the history of these curves and their mathematical properties reference should be made to Richards' paper. It suffices to say here that the family defined by (1) includes as special cases several curves which have been used empirically for the description of growth, including the 'monomolecular' (diminishing returns) curve (6 = -1), the exponential curve (6 -> 0 through positive values), the logistic curve (6 = 1), and the Gompertz curve (6 a) with A fixed and K a linear function of 0).