weib.fx: A function having the mathematical expression of the Weibull...
In biometrics: A Package for Biometrics and Modelling

weib.fx

R Documentation

A function having the mathematical expression of the Weibull allometric model.

Description

Function of the Weibull allometric model, based upon three parameters and a single predictor variable as follows

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

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

weib.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

Weibull W. 1951. A statistical distribution function of wide applicability. J. Appl. Mech.-Trans. ASME 18(3):293-297.
Yang RC, A Kozak, JH Smith. 1978. The potential of Weibull-type functions as flexible growth curves. Can. J. For. Res. 8(2):424-431.
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<-weib.fx(x=time,alpha=23.06,beta=.13,gamma=.63)
plot(time,y,type="l")

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