biometrics (version 1.0.3)

wykoff.fx: 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, a = alpha, b = beta, phi = 0)

Value

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

Arguments

x

is the predictor variable.

a

is the coefficient-parameter \(\alpha\).

b

is the coefficient-parameter \(\beta\).

phi

is an optional constant term that force the prediction of y when x=0. Thus, the new model becomes \( y_i = \phi+ f\left(x_i,\mathbf{\theta}\right)\), where \(\mathbf{\theta}\) is the vector of coefficients of the above described function represented by \(f(\cdot)\). The default value for \(\phi\) is 0.

Author

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,a=3.87,b=4.38,phi=1.3)
plot(d,h,type="l")