The Gompertz model for incremental data

The Gompertz curve was originally derived to estimate human mortality by Benjamin Gompertz (Gompertz, B. "On the Nature of the Function Expressive of the Law of Human Mortality, and on a New Mode of Determining the Value of Life Contingencies." Phil. Trans. Roy. Soc. London 123, 513-585, 1832). Charles Winsor (1932) presents an early description of the use of this equation to describe growth processes. There are a number of different ways that this equation can be written (see 3 parameter Gompertz growth equation). When using incremental data the version used is

where t is age 

where k is the growth rate

b a scaling parameter and

L∞, termed 'L infinity', is the asymptotic length at which growth is zero.