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

hossfeld.fx

R Documentation

Function that computes the result of the Hossfeld allometric model.

Description

Function of the Hossfeld (actually it is "Hoßfeld") allometric model, based upon parameters (i.e., coefficients) and a variable, as defined by the mathematical expression

y_i= \alpha \left(\frac{1}{1+\frac{\beta}{x_i^{\gamma}}}\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). Further details on this function can be found in Salas-Eljatib (2025).

Usage

hossfeld.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

Hoßfeld JW. 1822. Mathematik für Forstmänner, Oekonomen und Cameralisten. Dresden, Germany. Gotha:Hennings. 472 p.
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<-hossfeld.fx(x=time,alpha=31,beta=38,gamma=1.4)
plot(time,y,type="l")

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