scholarly journals Modeling Diameter Distribution of Black Alder (Alnus glutinosa (L.) Gaertn.) Stands in Poland

Forests ◽  
2019 ◽  
Vol 10 (5) ◽  
pp. 412 ◽  
Author(s):  
Piotr Pogoda ◽  
Wojciech Ochał ◽  
Stanisław Orzeł
Keyword(s):  
Goodness Of Fit ◽  
Mean Squared Error ◽  
Alnus Glutinosa ◽  
Weibull Model ◽  
Diameter Distribution ◽  
Stand Age ◽  
Weibull Function ◽  
Black Alder ◽  
Kolmogorov Smirnov ◽  
Non Parametric

We present diameter distribution models for black alder (Alnus glutinosa (L.) Gaertn.) derived from diameter measurements made at breast height in 844 circular sample plots set in 163 managed stands located in south-eastern Poland. A total of 22,530 trees were measured. Stand age ranged from six to 89 years. The model formulation was based on the two-parameter Weibull function and a non-parametric percentile-based method. Weibull function parameters were recovered from the first raw and second central moments estimated using the stand quadratic mean diameter. The same stand characteristic was used to predict values of 12 percentiles in the percentile-based method. The model performance was assessed using the k-fold cross-validation method. The goodness-of-fit statistics include the Kolmogorov–Smirnov statistic, mean error, root mean squared error, and two variants of the error index introduced by Reynolds. The percentile model developed, accurately predicted diameter distributions in 88.4% of black alder stands, as compared to 81.9% for the Weibull model (Kolmogorov–Smirnov test). Alternative statistical metrics assessing goodness-of-fit to empirical distributions suggested that the non-parametric percentile model was superior to the parametric Weibull model, especially in stands older than 20 years. In younger stands, the two models were accurate only in 57% of the cases, and did not differ significantly with respect to goodness-of-fit measures.

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

Forests ◽  
2020 ◽  
Vol 11 (6) ◽  
pp. 634 ◽  
Author(s):  
Piotr Pogoda ◽  
Wojciech Ochał ◽  
Stanisław Orzeł
Keyword(s):  
Mean Squared Error ◽  
Parametric Method ◽  
Kernel Estimator ◽  
Alnus Glutinosa ◽  
Diameter Distribution ◽  
Black Alder ◽  
Squared Error ◽  
Kolmogorov Smirnov ◽  
Test Sets ◽  
Anderson Darling

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.

Weibull diameter distributions for mixed stands of western conifers

1983 ◽  
Vol 13 (1) ◽  
pp. 85-88 ◽  
Author(s):  
Susan N. Little
Keyword(s):  
Goodness Of Fit ◽  
Test Group ◽  
Stand Age ◽  
Weibull Function ◽  
Prediction Equations ◽  
Mixed Stands ◽  
Forest Inventories ◽  
Kolmogorov Smirnov ◽  
Level Of Significance ◽  
Diameter Distributions

The three-parameter Weibull function met specified standards for goodness of fit as a model for the diameter distributions of mixed stands of western hemlock and Douglas-fir. Weibull distributions estimated by maximum likelihood (MLE) fit 80 of 83 observed diameter distributions at the α = 0.20 level of significance by the Kolmogorov–Smirnov test. Weibull parameter prediction equations were developed by regressing characteristics of 42 stands against MLE of the parameters. The Weibull diameter distributions predicted from stand age, mean diameter, mean height, and trees per acre (1 a = 100 m2) fit 39 of 41 observed distributions in the test group at the α = 0.20 level of significance. These results compared favorably with those found for various forest types by other authors. These prediction equations will prove useful in stand modeling and in updating forest inventories.

scholarly journals PROPOSTA METODOLÓGICA PARA O AJUSTE ÓTIMO DA DISTRIBUIÇÃO DIAMÉTRICA WEIBULL 3P

FLORESTA ◽  
2004 ◽  
Vol 34 (3) ◽  
Author(s):  
Oscar Santiago Vallejos Barra ◽  
Carlos Roberto Sanquetta ◽  
Julio Eduardo Arce ◽  
Sebastião Do Amaral Machado ◽  
Ana Paula Dalla Corte
Keyword(s):  
Maximum Likelihood ◽  
Probability Distribution ◽  
Goodness Of Fit ◽  
Location Parameter ◽  
Growth And Yield ◽  
Diameter Distribution ◽  
Weibull Function ◽  
Kolmogorov Smirnov ◽  
Two Parameters ◽  
Smirnov Test

A distribuição de Weibull de três parâmetros tem ampla utilização na área florestal. Existem três métodos para ajustar a distribuição, os quais consideram o parâmetro de locação como um termo independente que deve ser conhecido para obter os restantes parâmetros. Esta proposta metodológica visa, através de um processo interativo, otimizar o ajuste de cada um dos métodos mais utilizados para esta finalidade, sendo eles: máxima verossimilhança, momentos e percentis. Esta proposta visa minimizar o “dn” do teste de aderência de Kolmogorov-Smirnov. Observou-se que os valores de “dn” da distribuição Weibull de três parâmetros são inferiores aos obtidos na de dois parâmetros nos três métodos de ajuste. Observou-se ainda que os valores “dn” de cada método não apresentam diferenças expressivas, mas quando são comparadas as probabilidades associadas à magnitude tornam-se relevantes e justificam a metodologia proposta. Concluiu-se que esta nova metodologia é uma alternativa útil para ajuste de distribuições diamétricas e aplicações em modelagem do crescimento e da produção de povoamentos florestais. A NEW METHOD FOR THE OPTIMUM FITTING OF THE 3-P WEIBULL DIAMETER DISTRIBUTION Abstract The Weibull probability distribution of three parameters has wide use forestry. There are three fitting methods used for this purpose, which take into consideration the location parameter as an independent term that should be known previously to obtain the remaining parameters. This methodological proposal aims at showing an iterative method of optimization the fitting of the three parameters of the Weibull function in each one of the methods: maximum likelihood, moments, and percentiles. The proposed method minimizes the statistical “dn” of the Kolmogorov-Smirnov test of goodness-of-fit. It was noticed that “dn” of the three parameters Weibull distribution are lower than those of the two parameters function for the three fitting methods. It was also observed that “dn” values of each method were not significantly different one another, but when the probabilities were compared expressive differences were noticed, indicating the methodology is adequate. It was concluded that the new methodology is a useful alternative for the fitting of diameter distributions and application in modeling of growth and yield of forest stands.

scholarly journals Probability density functions for description of diameter distribution in thinned stands of Tectona grandis

CERNE ◽  
2012 ◽  
Vol 18 (2) ◽  
pp. 185-196 ◽  
Author(s):  
Daniel Henrique Breda Binoti ◽  
Mayra Luiza Marques da Silva Binoti ◽  
Helio Garcia Leite ◽  
Leonardo Fardin ◽  
Julianne de Castro Oliveira
Keyword(s):  
Fatigue Life ◽  
Goodness Of Fit ◽  
Basal Area ◽  
Tectona Grandis ◽  
Diameter Distribution ◽  
Permanent Plots ◽  
Weibull Function ◽  
Goodness Of Fit Test ◽  
Mato Grosso ◽  
Kolmogorov Smirnov

The objective of this study was to evaluate the effectiveness of fatigue life, Frechet, Gamma, Generalized Gamma, Generalized Logistic, Log-logistic, Nakagami, Beta, Burr, Dagum, Weibull and Hyperbolic distributions in describing diameter distribution in teak stands subjected to thinning at different ages. Data used in this study originated from 238 rectangular permanent plots 490 m² in size, installed in stands of Tectona grandis L. f. in Mato Grosso state, Brazil. The plots were measured at ages 34, 43, 55, 68, 81, 82, 92, 104, 105, 120, 134 and 145 months on average. Thinning was done in two occasions: the first was systematic at age 81months, with a basal area intensity of 36%, while the second was selective at age 104 months on average and removed poorer trees, reducing basal area by 30%. Fittings were assessed by the Kolmogorov-Smirnov goodness-of-fit test. The Log-logistic (3P), Burr (3P), Hyperbolic (3P), Burr (4P), Weibull (3P), Hyperbolic (2P), Fatigue Life (3P) and Nakagami functions provided more satisfactory values for the k-s test than the more commonly used Weibull function.

scholarly journals AJUSTE DA FUNÇÃO DE DISTRIBUIÇÃO DIAMÉTRICA WEIBULL POR PLANILHA ELETRÔNICA

FLORESTA ◽  
2011 ◽  
Vol 41 (2) ◽  
Author(s):  
William Thomaz Wendling ◽  
Dartagnan Baggio Emerenciano ◽  
Roberto Tuyoshi Hosokawa
Keyword(s):  
Distribution Function ◽  
Goodness Of Fit ◽  
Diameter Distribution ◽  
Goodness Of Fit Test ◽  
Function Model ◽  
Helpful Tool ◽  
Test Efficiency ◽  
Kolmogorov Smirnov ◽  
Electronic Spreadsheet ◽  
Main Model

Desenvolve-se uma metodologia traçada por um roteiro em algoritmo factível e amigável para efetivação em planilhas eletrônicas, reconhecidas como uma interface popular para cálculos. Busca-se, assim, apresentar uma ferramenta útil para alunos de graduação e recém-graduados em engenharia florestal, ou engenheiros mais experientes que ainda não dominem a técnica, para ajuste de um modelo de função densidade de probabilidade, com o objetivo de descrever a estrutura da distribuição diamétrica de populações florestais. O modelo adotado é o da função de Weibull, e o método de ajuste é o do percentis, com simulações comparadas por teste de aderência de Kolmogorov-Smirnov. A eficiência do método apresentado é testada por comparação a outro método alternativo.Palavras-chave:  Manejo florestal; florestas - modelos matemáticos; florestas - simulação por computador. AbstractWeibull diameter distribution function adjusts for electronic spreadsheet. This research develops a methodology based on easy and friendly algorithm for spreadsheets, a well known interface for calculus. It aims to present a helpful tool for forestry students, as well as for newly or experienced engineers who haven’t already known adjustment techniques for a density function model of probability, which is useful into diametric distribution structure descriptions of forest population. It has Weibull’s function as main model, percentile as adjustment method, and comparing simulations by Kolmogorov-Smirnov goodness-of-fit test. Efficiency of the presented method was tested by comparison to another method.Keywords: Forest management; forest - mathematical models; forest - computer simulator.

scholarly journals Predicting Diameter Distributions for Young Longleaf Pine Plantations in Southwest Georgia

2009 ◽  
Vol 33 (1) ◽  
pp. 25-28 ◽  
Author(s):  
Lichun Jiang ◽  
John R. Brooks
Keyword(s):  
Distribution Function ◽  
Goodness Of Fit ◽  
Longleaf Pine ◽  
Pinus Palustris ◽  
Cumulative Distribution ◽  
Diameter Distribution ◽  
Weibull Function ◽  
Recovery Method ◽  
Parameter Recovery ◽  
Diameter Distributions

Abstract Parameter prediction equations for the Weibull distribution function were developed based on four percentile functions and a parameter recovery method for longleaf pine (Pinus palustris Mill.) in Southwest Georgia. Four percentiles were expressed as functions of stand-level characteristics based on stepwise regression and seemingly unrelated regression. Using a percentile-based parameter recovery method (PCT), estimated diameter distributions were obtained from available stand-level variables. The PCT method was also compared with a cumulative distribution function (CDF) regression method. The PCT method produced consistently better goodness-of-fit statistics than the CDF method. The results indicate that diameter distribution in longleaf pine stands can be successfully characterized with the Weibull function.

Reliability Analysis of the Hydro-System of Excavator SchRs 800 Using Weibull Distribution

2015 ◽  
Vol 806 ◽  
pp. 173-180 ◽  
Author(s):  
Predrag Dašić ◽  
Milutin Živković ◽  
Marina Karić
Keyword(s):  
Weibull Distribution ◽  
Reliability Analysis ◽  
Goodness Of Fit ◽  
Weibull Model ◽  
Reliability Model ◽  
Goodness Of Fit Tests ◽  
Kolmogorov Smirnov ◽  
Von Mises

In this paper is given the use Weibull distribution (WD) as theoretical reliability model for analysis of the hydro-system of excavator SchRs 800, which is accepted on the basis of Pearson (χ2), Kolmogorov-Smirnov (KS) and Cramér-von Mises (CvM) goodness-of-fit tests. The time of work without failure of the hydro-system of excavator SchRs 800 for accepted Weibull model of reliability for probability of 50 % is T50%=0.3417⋅103[h], for probability of 80 % is T80%=0.1884⋅103[h] and for probability of 90% is T90%=0.127⋅103[h].

scholarly journals Models for diameter distribution and tree height in hybrid aspen plantations in southern Finland

Silva Fennica ◽  
2021 ◽  
Vol 55 (5) ◽  
Author(s):  
Daesung Lee ◽  
Jouni Siipilehto ◽  
Jari Hynynen
Keyword(s):  
Goodness Of Fit ◽  
Basal Area ◽  
Tree Height ◽  
Diameter Distribution ◽  
Weibull Function ◽  
Hybrid Aspen ◽  
Recovery Method ◽  
Parameter Recovery ◽  
Mean Diameter ◽  
Median Diameter

Hybrid aspen ( L. × Michx.) is known with outstanding growth rate and some favourable wood characteristics, but models for stand management have not yet been prepared in northern Europe. This study introduces methods and models to predict tree dimensions, diameter at breast height (dbh) and tree height for a hybrid aspen plantation using data from repeatedly measured permanent sample plots established in clonal plantations in southern Finland. Dbh distributions using parameter recovery method for the Weibull function was used with Näslund’s height curve to model tree heights. According to the goodness-of-fit statistics of Kolmogorov-Smirnov and the Error Index, the arithmetic mean diameter () and basal area-weighted mean diameter () provided more stable parameter recovery for the Weibull distribution than the median diameter () and basal area-weighted median diameter (), while showed the best overall fit. Thus, Näslund’s height curve was modelled using with Lorey’s height (), age, basal area (), and tree dbh (Model 1). Also, Model 2 was tested using all predictors of Model 1 with the number of trees per ha (). All predictors were shown to be significant in both Models, showing slightly different behaviour. Model 1 was sensitive to the mean characteristics, and , while Model 2 was sensitive to stand density, including both and as predictors. Model 1 was considered more reasonable to apply based on our results. Consequently, the parameter recovery method using and Näslund’s models were applicable for predicting tree diameter and height.Populus tremulaP. tremuloidesDDGDMDGMDGDGHGBATPHDGHGBATPHDG

Predicting Crown Sizes and Diameter Distributions of Tanoak, Pacific Madrone, and Giant Chinkapin Sprout Clumps

1992 ◽  
Vol 7 (4) ◽  
pp. 103-108 ◽  
Author(s):  
Timothy B. Harrington ◽  
John C. Tappeiner ◽  
Ralph Warbington
Keyword(s):  
Goodness Of Fit ◽  
Basal Area ◽  
Diameter Distribution ◽  
Weibull Function ◽  
Regression Equations ◽  
Growing Seasons ◽  
Lithocarpus Densiflorus ◽  
Pacific Madrone ◽  
Crown Size ◽  
Diameter Distributions

Abstract Crown size and stem diameters were measured on a total of 908 sprout clumps of tanoak (Lithocarpus densiflorus), Pacific madrone (Arbutus menziesii), and giant chinkapin (Castanopsis chrysophylla). The clumps, age 1 to 16 years, were located at 23 sites in southwestern Oregon and 20 sites in northwestern California. Regression equations were developed for predicting individual-clump crown size and stem-diameter distributions of dominant sprouts from the total basal area (dm² at 1.37 m) in stems of the parent tree (PBA) and number of growing seasons since burning (AGE). Variables of PBA, AGE, and species in combination accounted for over 75% of the total variation in hardwood crown width and height and for 62% of the variation in sprout number. Variables describing site characteristics and competing vegetation abundance did not explain more than 2% of additional variation in hardwood crown size or sprout diameter distribution. On the basis of the Kolmogorov-Smirnoff test (α = 0.05), the Weibull function adequately described the reverse J-shaped distribution of stem diameters for individual sprout clumps. The goodness of fit for each of the predictive models for tanoak and madrone was verified with independent data. West. J. Appl. For. 7(4):103-108.

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