iForest - Biogeosciences and Forestry


Evaluation of estimation methods for fitting the three-parameter Weibull distribution to European beech forests

Ziva Bončina (1-2), Vasilije Trifković (1), Christian Rosset (3), Matija Klopčič (1)   

iForest - Biogeosciences and Forestry, Volume 15, Issue 6, Pages 484-490 (2022)
doi: https://doi.org/10.3832/ifor4145-015
Published: Dec 01, 2022 - Copyright © 2022 SISEF

Research Articles

We evaluated three estimation methods for fitting the three-parameter Weibull distribution to even-aged European beech (Fagus sylvatica) forests by using experimental tree diameter data collected in 3709 sample plots (500 m2 each). The maximum likelihood estimation method (MLE), the method of moments (MOM) and the method of modified moments type 1 (MM1) were applied for fitting the Weibull function. The goodness-of-fit of stand parameters (total tree number, stand basal area, dominant stand diameter and mean quadratic diameter) was tested by MAE and RMSE, and the probability and cumulative density functions of trees per 5 cm diameter classes were additionally tested by the Kolmogorov-Smirnov test and compared with Kolmogorov-Smirnov’s D statistic. All three methods are suitable for estimating stand parameters based on the fitted Weibull function. Fitting the diameter distribution per 5 cm diameter classes at the plot level was less accurate due to the low number of trees or irregular diameter distribution of trees. The MM1 method was found to be the most suitable for fitting the three-parameter Weibull distribution to beech forests represented by data derived from small plots.


Diameter Distribution Fitting, Weibull Function, Parameter Estimation, Inventory Data, Circular Sample Plots, Near-natural Forests, Fagus Sylvatica, Slovenia

Authors’ address

Ziva Bončina
Vasilije Trifković 0000-0002-7533-5708
Matija Klopčič 0000-0003-2619-9073
Department of Forestry and Renewable Forest Resources, Biotechnical Faculty, University of Ljubljana, Večna pot 83, 1000 Ljubljana (Slovenia)
Ziva Bončina
Slovenia Forest Service, Večna pot 2, 1000 Ljubljana (Slovenia)
Christian Rosset
Forest Ecosystem and Management, School of Agricultural, Forest and Food Sciences, HAFL, Bern University of Applied Sciences, Länggasse 85, 3052 Zollikofen (Switzerland)

Corresponding author

Matija Klopčič


Bončina Z, Trifković V, Rosset C, Klopčič M (2022). Evaluation of estimation methods for fitting the three-parameter Weibull distribution to European beech forests. iForest 15: 484-490. - doi: 10.3832/ifor4145-015

Academic Editor

Andrea Cutini

Paper history

Received: May 30, 2022
Accepted: Sep 27, 2022

First online: Dec 01, 2022
Publication Date: Dec 31, 2022
Publication Time: 2.17 months

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