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

wykoff.fx

R Documentation

A function having the mathematical expression of the Wykoff model.

Description

Function of the Wykoff model, based upon two parameters and a single predictor variable as follows

y_i= \mathrm{e}^{\left(\alpha+\frac{\beta}{x_i+1} \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

wykoff.fx(x, alpha, beta, upsilon = 0)

Arguments

`x`	is the predictor variable.
`alpha`	is the coefficient-parameter `\alpha`.
`beta`	is the coefficient-parameter `\beta`.
`upsilon`	is an optional constant term that force the prediction of y when x=0. Thus, the new model becomes `y_i = \Upsilon+ f\left(x_i,\mathbf{\theta}\right)`, 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

Wykoff WR, NL Crookston, AR Stage. 1982. User’s guide to the Stand Prognosis Model. USDA For. Serv. Gen. Tech. Rep. INT-133, USA. 112 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
d<-seq(5,60,by=0.01)
# Using the function
h<-wykoff.fx(x=d,alpha=3.87,beta=4.38,upsilon=1.3)
plot(d,h,type="l")

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