iForest - Biogeosciences and Forestry


Properties and prediction accuracy of a sigmoid function of time-determinate growth

Róbert Sedmák (1-2), Lubomír Scheer (1)   

iForest - Biogeosciences and Forestry, Volume 8, Issue 5, Pages 631-637 (2015)
doi: https://doi.org/10.3832/ifor1243-007
Published: Jan 13, 2015 - Copyright © 2015 SISEF

Research Articles

The properties and short-term prediction accuracy of mathematical model of sigmoid time-determinate growth, denoted as “KM-function”, are presented. Comparative mathematical analysis of the function revealed that it is a model of asymmetrical sigmoid growth, which starts at zero size of an organism and terminates when it reaches its final size. The function assumes a finite length of the growth period and includes a parameter interpretable as the expected lifespan of the organism. Moreover, the possibility for growth curve inflexion at any age is possible, so the function can be used for modelling of S-shaped growth trajectories with various degree of asymmetry. These good theoretical predispositions for realistic growth predictions were empirically evaluated. The KM-function used in three and four-parameter forms was compared with three classical (Richards, Korf and Weibull) growth functions employing two parameterisation methods - nonlinear least squares (NLS) and Bayesian method. The evaluation was conducted on the basis of the tree diameter series obtained from stem analyses. The main empirical findings are: (i) if the minimisation of the prediction bias is required, the KM-function in three-parameter form in connection with Bayes parameterisation can be recommended; (ii) if the minimisation of root square error (RMSE) is required, the best short-term prediction results for a particular dataset were obtained with four-parameter Weibull function employing NLS parameterisation; (iii) moreover, three-parameter functions parameterised by Bayesian methods show a considerably smaller RMSE by 15-25% as well as smaller biases by 40-60% than four-parameter functions employing NLS. Overall, all analyses confirmed relative usefulness of the KM-function in comparison with classical growth functions, especially in connection with Bayesian parameterisation.


Growth Function, Determinate Growth, Nonlinear Least Squares, Bayes, Prediction

Authors’ address

Róbert Sedmák
Lubomír Scheer
Faculty of Forestry, Technical University in Zvolen, T.G. Masaryka 24, 960 53 Zvolen (Slovak Republic)
Róbert Sedmák
Faculty of Forestry and Wood Sciences, Czech University of Life Sciences Prague, Kamýcká 1176, 165 21 Praha 6 - Suchdol (Czech Republic)

Corresponding author

Lubomír Scheer


Sedmák R, Scheer L (2015). Properties and prediction accuracy of a sigmoid function of time-determinate growth. iForest 8: 631-637. - doi: 10.3832/ifor1243-007

Academic Editor

Renzo Motta

Paper history

Received: Jan 15, 2014
Accepted: Oct 17, 2014

First online: Jan 13, 2015
Publication Date: Oct 01, 2015
Publication Time: 2.93 months

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