ogawa.fx: Function that computes the result of the Ogawa allometric...
In biometrics: A Package for Biometrics and Modelling

ogawa.fx

R Documentation

Function that computes the result of the Ogawa allometric model.

Description

Function of the Ogawa allometric model, based upon parameters (i.e., coefficients) and a variable, as defined by the mathematical expression

{y_i}= \left(\frac{1}{\alpha} + \frac{1}{\beta {x_i}^{\gamma}}\right)^{-1},

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). Further details on this function can be found in Salas-Eljatib (2025).

Usage

ogawa.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 inverse of the response variable based upon the predictor variable and the coefficients shown above.

Author(s)

Christian Salas-Eljatib.

References

Kohyama T, T Hara, T Tadaki. 1990. Patterns of trunk diameter, tree height and crown depth in crowded abies stands. Annals of Botany 65(5):567–574.
Salas-Eljatib C. 2026. 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. 53 p. https://biometriaforestal.uchile.cl

Examples

# Predictor variable values to be used
time<-seq(5,60,by=0.01)
# Using the function
d<-ogawa.fx(x=time,alpha=22,beta=0.013,gamma=1.13)
plot(time,d,type="l")

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