Sigmoidal Relationship

A verbal description of the relationship

A sigmoidal curve starts out with a low slope, increases the slope to an inflection point, then levels off as it approaches a maximum value.

There are two mechanisms that can cause this type of curve that will be mentioned here:

saturating hyperbola with X to some power

the "logistic equation"

The equation and the meaning of x, y, and other parameters

Y = m * X^n/(X^n + K^n)

please see the description of the "logistic" equation in the notes.

One or more examples

to be added later

A graph

Algebraic rules that apply to the use of this equation

The power function is calculated before multiplication or division.

Characteristic values

For this equation Y = m * X^n/(X^n + K^n)

Y ranges from 0 to m

at X = 0, Y = 0

at X = K, Y = m/2

for small X, the curve is more concave that for a simple saturating hyperbola

increasing values of n, make the sigmoidal shape more prominent.