Performance of Kernel Estimator and Johnson S<sub>B</sub> Function for Modeling Diameter Distribution of Black Alder (<i>Alnus glutinosa</i> (L.) Gaertn.) Stands
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). Jo...
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MDPI AG
2020-06-01
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| Online Access: | https://www.mdpi.com/1999-4907/11/6/634 |
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| author | Piotr Pogoda Wojciech Ochał Stanisław Orzeł |
| author_facet | Piotr Pogoda Wojciech Ochał Stanisław Orzeł |
| author_sort | Piotr Pogoda |
| collection | DOAJ |
| description | 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 S<sub>B</sub> (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 (<i>Alnus glutinosa</i> (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. |
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| spelling | doaj.art-f089c12994f54cfcb4449af39217f62f2023-11-20T02:42:00ZengMDPI AGForests1999-49072020-06-0111663410.3390/f11060634Performance of Kernel Estimator and Johnson S<sub>B</sub> Function for Modeling Diameter Distribution of Black Alder (<i>Alnus glutinosa</i> (L.) Gaertn.) StandsPiotr Pogoda0Wojciech Ochał1Stanisław Orzeł2Department of Forest Resources Management, Faculty of Forestry, University of Agriculture in Krakow, Al. 29 Listopada 46, 31-425 Krakow, PolandDepartment of Forest Resources Management, Faculty of Forestry, University of Agriculture in Krakow, Al. 29 Listopada 46, 31-425 Krakow, PolandDepartment of Forest Resources Management, Faculty of Forestry, University of Agriculture in Krakow, Al. 29 Listopada 46, 31-425 Krakow, PolandWe 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 S<sub>B</sub> (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 (<i>Alnus glutinosa</i> (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.https://www.mdpi.com/1999-4907/11/6/634diameter distributionkernel estimatorJohnson S<sub>B</sub> functionblack alder |
| spellingShingle | Piotr Pogoda Wojciech Ochał Stanisław Orzeł Performance of Kernel Estimator and Johnson S<sub>B</sub> Function for Modeling Diameter Distribution of Black Alder (<i>Alnus glutinosa</i> (L.) Gaertn.) Stands Forests diameter distribution kernel estimator Johnson S<sub>B</sub> function black alder |
| title | Performance of Kernel Estimator and Johnson S<sub>B</sub> Function for Modeling Diameter Distribution of Black Alder (<i>Alnus glutinosa</i> (L.) Gaertn.) Stands |
| title_full | Performance of Kernel Estimator and Johnson S<sub>B</sub> Function for Modeling Diameter Distribution of Black Alder (<i>Alnus glutinosa</i> (L.) Gaertn.) Stands |
| title_fullStr | Performance of Kernel Estimator and Johnson S<sub>B</sub> Function for Modeling Diameter Distribution of Black Alder (<i>Alnus glutinosa</i> (L.) Gaertn.) Stands |
| title_full_unstemmed | Performance of Kernel Estimator and Johnson S<sub>B</sub> Function for Modeling Diameter Distribution of Black Alder (<i>Alnus glutinosa</i> (L.) Gaertn.) Stands |
| title_short | Performance of Kernel Estimator and Johnson S<sub>B</sub> Function for Modeling Diameter Distribution of Black Alder (<i>Alnus glutinosa</i> (L.) Gaertn.) Stands |
| title_sort | performance of kernel estimator and johnson s sub b sub function for modeling diameter distribution of black alder i alnus glutinosa i l gaertn stands |
| topic | diameter distribution kernel estimator Johnson S<sub>B</sub> function black alder |
| url | https://www.mdpi.com/1999-4907/11/6/634 |
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