A Gompertz curve, nmamed after Benjamin Gompertz, is a type of mathematical model for a time series, where growth is slowest at the start and end of a time period.

$y(t)=ae^\{be^\{ct\}\}$

where

• a is the upper asymptote
• c is the growth rate
• b, c are negative numbers
• e is the base of the natural logarithm (e = 2.71828...)

Examples of uses for Gompertz curves include:

• Mobile phone uptake, where costs were initially high (so uptake was slow), followed by a period of rapid growth, followed by a slowing of uptake as saturation was reached.
• Population in a confined space, as birth rates first increase and then slow as resource limits are reached.

See also

• Logistic function
• Gompertz-Makeham law of mortality

信頼度成長曲線

Curves