Generalization and Reparameterization of Some Sigmoid and Other Nonlinear Functions

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Abstract
Many functions used in describing growth can be derived from a single new function that is a power of the difference between a weighted elementary function and a power of its exponential. Furthermore, new parameters are suggested for the simplest 2-asymptote, 3rd-degree form of the Pearl-Reed function so that parameters specifying curvature are made independent of those specifying location of point of inflection. Finally, general expressions for derivatives, partial derivatives, and points of inflections are given in terms of new parameters for both the new growth function and the Pearl-Reed function to facilitate computer improvement of parameters appropriate to a given set of observed data.

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