biometrics (version 1.0.3)

lang.fx: Function to computes the result of the Curtis's allometric model.

Description

Function of the Langhmuir model, based upon two parameters, and a single predictor variable, as follows $$y_i= \alpha \left(\frac{1}{1+\frac{1}{\beta x_i}}\right),$$ 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 of this function can be found in Salas-Eljatib (2025).

Usage

lang.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 \( y_i = \phi+ f(x_i,\mathbf{\theta})\), where \(\mathbf{\theta}\) is the vector of coefficients of the above described function represented by \(f(\cdot)\). The default value for \(\phi\) is 0.

Author

Christian Salas-Eljatib.

References

• Khayyun TS, Mseer AH. 2019. Comparison of the experimental results with the Langmuir and Freundlich models for copper removal on limestone adsorbent. Applied Water Science 9(8):170.

• 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(.1,60,by=0.01)
# Using the function
y<-lang.fx(x=time, a=37,b=0.05)
plot(time,y,type="l")