schum.fx: A function having the mathematical expression of the...

In biometrics: A Package for Biometrics and Modelling

A function having the mathematical expression of the Johnson-Schumacher model.

Description

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

y_i= \alpha \mathrm{e}^{\left(-\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 on this model can be found in Salas-Eljatib et al (2021) and Salas-Eljatib (2025).

Usage

schuma.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(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

• Johnson NO. 1935. A trend line for growth series. J. Am. Stat. Assoc. 30(192):717-717.

• Schumacher FX. 1939. A new growth curve and its application to timber yield studies. J. of Forestry 37(10):819-820.

• Salas-Eljatib C, Mehtatalo L, Gregoire TG, Soto DP, Vargas-Gaete R. 2021. Growth equations in forest research: mathematical basis and model similarities. Current Forestry Reports 7:230-244. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s40725-021-00145-8")}

• 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<-schuma.fx(x=d,alpha=3.87,beta=4.38)
plot(d,h,type="l")
 

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