Editing Generalised logistic function (section)

==Definition==
Richards's curve has the following form:
:<math>Y(t) = A + { K-A \over (C + Q e^{-B t}) ^ {1 / \nu} }</math>
where <math>Y</math> = weight, height, size etc., and <math>t</math> = time. It has six parameters:
*<math>A</math>: the left horizontal asymptote;
*<math>K</math>: the right horizontal asymptote when <math>C=1</math>. If <math>A=0</math> and <math>C=1</math> then <math>K</math> is called the [[carrying capacity]];
*<math>B</math>: the growth rate;
*<math>\nu > 0</math> : affects near which asymptote maximum growth occurs.
*<math>Q</math>: is related to the value <math>Y(0)</math>
*<math>C</math>: typically takes a value of 1. Otherwise, the upper asymptote is <math>A + {K - A \over C^{\, 1 / \nu}}</math>

The equation can also be written:

:<math>Y(t) = A + { K-A \over (C + e^{-B(t - M)}) ^ {1 / \nu} }</math>

where <math>M</math> can be thought of as a starting time, at which <math>Y(M) = A + { K-A \over (C+1) ^ {1 / \nu} }</math>. Including both <math>Q</math> and <math>M</math> can be convenient:

:<math>Y(t) = A + { K-A \over (C + Q e^{-B(t - M)}) ^ {1 / \nu} }</math>

this representation simplifies the setting of both a starting time and the value of <math>Y</math> at that time.

The [[logistic function]], with maximum growth rate at time <math>M</math>, is the case where <math>Q = \nu = 1</math>.