The Gudermannian Growth Model: Theory, Application and Statistical Analysis

HIGHLIGHTS

• This work introduces the Gudermannian function as a sigmoid growth model.

• Hyperbolic and trigonometric identities provide several parameterizations of this model.

• The Gudermannian growth model can be a good alternative to the classical sigmoid models.

Abstract:

Processes producing sigmoid curves are common in many areas such as biology, agrarian sciences, demography and engineering. Several mathematical functions have been proposed for modeling sigmoid curves. Some models such as the logistic, Gompertz, Richards and Weibull are widely used. This work introduces the Gudermannian function as an option for modeling sigmoid growth curves. The original function was transformed and the resulting equation was called the “Gudermannian growth model.” This model was applied to four sets of experimental growth data to illustrate its practical application. The results were compared with those obtained by the logistic and Gompertz models. Since all these models are nonlinear in the parameters, the statistical properties of the least squares estimators were evaluated using measures of nonlinearity. For each experimental data set, the Akaike’s corrected information criterion was utilized to discriminate among the models. In general, the Gudermannian model fitted better to the experimental data than the logistic and Gompertz models. The results showed that the Gudermannian model can be a good alternative to the classical sigmoid models.

Keywords:
Gudermannian function; sigmoid growth models; logistic model; Gompertz model; measures of nonlinearity