A class of sigmoid, monotonic curves, often used to model the growth of biological subjects. Three types of growth curve are
provided in GenStat, all types of logistic.
Logistic
Y = a + c/(1 + e-b(X-m)) ( Y = a + c / (1 + EXP(-b * (X-m))) )
Generalized logistic
Y = a + c(1 + te-b(X-m))-1/t ( Y = a + c / (1 + t * EXP(-b*(X-m)))**1/t )
Gompertz
Y = a + ce-e-b(X-m) ( Y = a + c * EXP(-EXP(-b * (X-m))) )
An asymmetrical s-shaped curve.
Direction of Response
For the Gompertz curve, the direction of response can be selected. The effect of direction on the parameters of the curves is
as follows: when b > 0, direction right gives c > 0 and direction left gives c < 0. However, when b < 0 this is reversed: see
Examples of Standard Nonlinear Curves for a graphical illustration.
See Also