The generalised logistic curve, also known as Richards' curve is a widely-used and flexible function for growth modelling.

$Y\; =\; A\; +\; \{\; C\; \backslash over\; (1\; +\; T\; e^\{-B\; (X\; -\; M)\})\; ^\; \{1\; /\; T\}\; \}$

where Y = weight, height, size etc., and X = time.

It has five parameters:

• A: the lower asymptote;
• C: the upper asymptote minus A;
• M: the time of maximum growth;
• B: the growth rate;
• T: affects near which asymptote maximum growth occurs.

References

• Richards, F.J. 1959 A flexible growth function for empirical use. J. Exp. Bot. 10: 290--300.
• Pella JS and PK Tomlinson. 1969. A generalised stock-production model. Bull. IATTC 13: 421-496.

See also

• Logistic function

Curves