The Gompertz model for incremental data
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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.