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This growth curve was originally proposed by Janoschek, A. (1957). The form of the equation used by Growth II can have initial values greater than 0 and was originally described by Sager (1978). It has the equation:
where l = length, (or weight, height, size) and t = time.
The four parameters are:
β, is the lower asymptote;
δ, is a parameter that controls the x-ordinate for the point of inflection.
Note that this curve is extremely similar to the Weibull growth curve.
The Janoschek growth curve has the flexibility of the Richards curve, but is far easier to fit and manipulate. It rarely fails to converge during non-linear regression.