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

doi:10.3832/ifor4145-015

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

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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.

Keywords

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

Authors’ address

(1)

0000-0002-7533-5708
0000-0003-2619-9073
Department of Forestry and Renewable Forest Resources, Biotechnical Faculty, University of Ljubljana, Večna pot 83, 1000 Ljubljana (Slovenia)

(2)

Slovenia Forest Service, Večna pot 2, 1000 Ljubljana (Slovenia)

(3)

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
matija.klopcic@bf.uni-lj.si

Citation

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

Open Access

This article is distributed under the terms of the Creative Commons Attribution-Non Commercial 4.0 International (https://creativecommons.org/licenses/by-nc/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

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