grex --- Growth-curve Explorer

Up to shifts and scaling, many growth curve and probability distribution functions having a closed form are special cases of $y = \varphi[\varphi(t, b), a]$, where $\varphi(x, \lambda) = (1 + \lambda x)^{1/\lambda}$ if $\lambda \ne 0$, $\varphi(x, 0) = \exp(-x)$, and $a \le 1$ and $b \le 1$ are shape parameters.

The Growth-curve Explorer is a visualization of this unifying equation. The original version is a Java applet described by García (2008), and available at https://web.unbc.ca/~garcia/growth&yield/grex/ (note that the original link through forestgrowth.unbc.ca is broken). Unfortunately, modern web browsers have dropped support for Java applets. Here are two alternatives:

1. A translation of the applet into JavaScript by CheerpJ. The code is in folder docs in this repository, and the app can be accessed at https://ogarciav.github.io/grex/ (be patient, loading can take a while). The original documentation has been slightly edited.

2. A re-implementation as an R Shiny app, in folder shiny. The app can be run on https://oscargarcia.shinyapps.io/grex/.

A third possibility is to run the Java applet from the original web site with the CheerpJ Chrome browser plugin.

For completeness, the old Java code is in folder original, including a stand-alone Java app. All the code in this repository is in the public domain.

The resde R package includes the unifying model as function unitran(), and implements some estimation methods.

References

• Chakraborty, B., Bhowmick, A. R., Chattopadhyay, J. and Bhattacharya, S. (2019). "A novel unification method to characterize a broad class of growth curve models using relative growth rate". Bulletin of Mathematical Biology 81, 2529-2552 DOI.

• García, O. (2005). "Unifying sigmoid univariate growth equations". Forest Biometry, Modelling and Information Sciences 1, 63-68 link.

• García, O. (2008). "Visualization of a general family of growth functions and probability distributions --- The Growth-curve Explorer". Environmental Modelling and Software 23 (12), 1474-1475 DOI.