gompertz.fx: Function to compute the result of the Gompertz allometric...
In biometrics: A Package for Biometrics and Modelling

gompertz.fx

R Documentation

Function to compute the result of the Gompertz allometric model.

Description

Function of the Gompertz model, depending on its three parameters and a variable, defined by the following mathematical expression

y_i= \alpha \mathrm{e}^{\left(-\beta \mathrm{e}^{-\gamma x_i} \right)},

where: y_i and x_i are the response and predictor variable, respectively for the i-th observation; and the rest are parameters (i.e., coefficients).

Usage

gompertz.fx(x, alpha, beta, gamma, upsilon = 0)

Arguments

`x`	is the predictor variable.
`alpha`	is the coefficient-parameter `\alpha`.
`beta`	is the coefficient-parameter `\beta`.
`gamma`	is the coefficient-parameter `\gamma`.
`upsilon`	is an optional constant term that force the prediction of y when x=0. Thus, the new model becomes `y_i = \Upsilon+ f(x_i,\mathbf{\theta})`, where `\mathbf{\theta}` is the vector of coefficients of the above described function represented by `f(\cdot)`. The default value for `\Upsilon` is 0.

Value

Returns the response variable based upon the predictor variable and the coefficients.

Author(s)

Christian Salas-Eljatib.

References

Gompertz B. 1825. 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. Philosophical Transactions of the Royal Society of London 115:513–583.
Salas-Eljatib C, Mehtatalo L, Gregoire TG, Soto DP, Vargas-Gaete R. 2021. Growth equations in forest research: mathematical basis and model similarities. Current Forestry Reports 7:230-244. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s40725-021-00145-8")}
Salas-Eljatib C. 2025. Funciones alométricas: reparametrizaciones y características matemáticas. Documento de trabajo No. 1, Serie: Cuadernos de biometría, Laboratorio de Biometría y Modelación Forestal, Universidad de Chile. Santiago, Chile. 51 p. https://biometriaforestal.uchile.cl

Examples

# Predictor variable values to be used
time<-seq(5,60,by=0.01)
# Using the function
y<-gompertz.fx(x=time,alpha=25,beta=.22,gamma=16)
plot(time,y,type="l")

biometrics documentation built on March 20, 2026, 5:09 p.m.