Performance of Kernel Estimator and Johnson SB Function for Modeling Diameter Distribution of Black Alder (Alnus glutinosa (L.) Gaertn.) Stands

Piotr Pogoda , Wojciech Ochał , Stanisław Orzeł


We compare the usefulness of nonparametric and parametric methods of diameter distribution modeling. The nonparametric method was represented by the new tool—kernel estimator of cumulative distribution function with bandwidths of 1 cm (KE1), 2 cm (KE2), and bandwidth obtained automatically (KEA). Johnson SB (JSB) function was used for the parametric method. The data set consisted of 7867 measurements made at breast height in 360 sample plots established in 36 managed black alder (Alnus glutinosa (L.) Gaertn.) stands located in southeastern Poland. The model performance was assessed using leave-one-plot-out cross-validation and goodness-of-fit measures: mean error, root mean squared error, Kolmogorov–Smirnov, and Anderson–Darling statistics. The model based on KE1 revealed a good fit to diameters forming training sets. A poor fit was observed for KEA. Frequency of diameters forming test sets were properly fitted by KEA and poorly by KE1. KEA develops more general models that can be used for the approximation of independent data sets. Models based on KE1 adequately fit local irregularities in diameter frequency, which may be considered as an advantageous in some situations and as a drawback in other conditions due to the risk of model overfitting. The application of the JSB function to training sets resulted in the worst fit among the developed models. The performance of the parametric method used to test sets varied depending on the criterion used. Similar to KEA, the JSB function gives more general models that emphasize the rough shape of the approximated distribution. Site type and stand age do not affect the fit of nonparametric models. The JSB function show slightly better fit in older stands. The differences between the average values of Kolmogorov–Smirnov (KS), Anderson–Darling (AD), and root mean squared error (RMSE) statistics calculated for models developed with test sets were statistically nonsignificant, which indicates the similar usefulness of the investigated methods for modeling diameter distribution.
Author Piotr Pogoda (FoF / IoFRM)
Piotr Pogoda,,
- Institute of Forest Resources Management
, Wojciech Ochał (FoF / Department of Forest Resource Management)
Wojciech Ochał,,
- Department of Forest Resource Management
, Stanisław Orzeł (FoF / Department of Forest Resource Management)
Stanisław Orzeł,,
- Department of Forest Resource Management
Journal seriesForests, ISSN 1999-4907, (N/A 100 pkt)
Issue year2020
Article number634
Keywords in Englishdiameter distribution; kernel estimator; Johnson SB function; black alder
ASJC Classification1107 Forestry
Languageen angielski
LicenseJournal (articles only); published final; Uznanie Autorstwa (CC-BY); with publication
Performance of Kernel Estimator and Johnson SB Function for Modeling Diameter Distribution of Black Alder (Alnus glutinosa (L.) Gaertn.) Stands of 10-06-2020
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Score (nominal)100
Score sourcejournalList
Publication indicators Scopus SNIP (Source Normalised Impact per Paper): 2018 = 0.943; WoS Impact Factor: 2018 = 2.116 (2) - 2018=2.453 (5)
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FinansowanieThis research was funded by the Ministry of Science and Higher Education (MNiSW, Poland) as statutory funds no. SUB/040015/D019 and carried out at the Department of Forest Resources Management, Faculty of Forestry, University of Agriculture in Krakow, Poland.
Wkład autorówConceptualization, P.P., W.O., and S.O.; methodology, P.P., W.O., and S.O.; software, P.P. and W.O.; validation, P.P. and W.O.; formal analysis, P.P. and W.O.; resources, S.O.; writing—original draft preparation, P.P.; writing—review and editing, W.O. and S.O. All authors have read and agreed to the published version of the manuscript
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