Generalised logistic function

The generalised logistic function or curve, also known as Richards' curve, originally developed for growth modelling, is an extension of the logistic or sigmoid functions, allowing for more flexible S-shaped curves:

where ${\displaystyle Y}$ = weight, height, size etc., and ${\displaystyle t}$ = time.

It has five parameters:

The equation can also be written:

where ${\displaystyle M}$ can be thought of a starting time, ${\displaystyle t_{0}}$ (at which ${\displaystyle Y(t_{0})=A+{K-A \over (C+1)^{1/\nu }}}$ )

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