Overview
The generalized logistic function or curve is an extension of the logistic or sigmoid functions. Originally developed for growth modelling, it allows for more flexible S-shaped curves. The function is sometimes named Richards's curve after F. J. Richards, who proposed the general form for the family of models in 1959.
Definition
Richards's curve has the following form:
where = weight, height, size etc., and = time. It has six parameters:
: the left horizontal asymptote;
: the right horizontal asymptote when . If and then is called the carrying capacity;
: the growth rate;
: affects near which asymptote maximum growth occurs.
: is related to the value
: typically takes a value of 1. Otherwise, the upper asymptote is
The equation can also be written:
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