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 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 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.

scholarly journals Modeling of short duration extreme rainfall events over Lower Yamuna Catchment

MAUSAM ◽  
2022 ◽  
Vol 63 (3) ◽  
pp. 391-400
Author(s):  
MEHFOOZ ALI ◽  
SURINDER KAUR ◽  
S.B. TYAGI ◽  
U.P. SINGH
Keyword(s):  
Short Duration ◽  
Goodness Of Fit ◽  
Extreme Rainfall ◽  
Return Periods ◽  
Goodness Of Fit Test ◽  
Extreme Rainfall Events ◽  
Rainfall Events ◽  
Kolmogorov Smirnov ◽  
Level Of Significance ◽  
Made In

Short duration rainfall estimates and their intensities for different return periods are required for many purposes such as for designing flood for hydraulic structures, urban flooding etc. An attempt has been made in this paper to Model extreme rainfall events of Short Duration over Lower Yamuna Catchment. Annual extreme rainfall series and their intensities were analysed using EVI distribution for rainstorms of short duration of 5, 10, 15, 30, 45 & 60 minutes and various return periods have been computed. The Self recording rainguage (SRRGs) data for the period 1988-2009 over the Lower Yamuna Catchment (LYC) have been used in this study. It has been found that EVI distribution fits well, tested by Kolmogorov-Smirnov goodness of fit test at 5 % level of significance for each of the station.

scholarly journals On the approximation of the concentration parameter for von Mises distribution

2017 ◽  
Vol 13 (4-1) ◽  
pp. 390-393
Author(s):  
Nor Hafizah Moslim ◽  
Yong Zulina Zubairi ◽  
Abdul Ghapor Hussin ◽  
Siti Fatimah Hassan ◽  
Rossita Mohamad Yunus
Keyword(s):  
Goodness Of Fit ◽  
Von Mises Distribution ◽  
Concentration Parameter ◽  
Normal Behavior ◽  
Kolmogorov Smirnov ◽  
Asymptotic Normal ◽  
Level Of Significance ◽  
Von Mises ◽  
Two Parameters ◽  
Relationship Of

The von Mises distribution is the ‘natural’ analogue on the circle of the Normal distribution on the real line and is widely used to describe circular variables. The distribution has two parameters, namely mean direction,  and concentration parameter, κ. Solutions to the parameters, however, cannot be derived in the closed form. Noting the relationship of the κ to the size of sample, we examine the asymptotic normal behavior of the parameter. The simulation study is carried out and Kolmogorov-Smirnov test is used to test the goodness of fit for three level of significance values. The study suggests that as sample size and concentration parameter increase, the percentage of samples follow the normality assumption increase. 

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.

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.

A Blind Spot in the Use of the Weibull Function for Modeling Diameter Distributions

2020 ◽  
Author(s):  
Adrian Norman Goodwin
Keyword(s):  
Lower Bound ◽  
Blind Spot ◽  
Forest Growth ◽  
Growth And Yield ◽  
Diameter Distribution ◽  
Absolute Difference ◽  
Weibull Function ◽  
Distribution Models ◽  
Difference Statistic ◽  
Diameter Distributions

Abstract Diameter distribution models based on probability density functions are integral to many forest growth and yield systems, where they are used to estimate product volumes within diameter classes. The three-parameter Weibull function with a constrained nonnegative lower bound is commonly used because of its flexibility and ease of fitting. This study compared Weibull and reverse Weibull functions with and without a lower bound constraint and left-hand truncation, across three large unthinned plantation cohorts in which 81% of plots had negatively skewed diameter distributions. Near-optimal lower bounds for the unconstrained Weibull function were negative for negatively skewed data, and the left-truncated Weibull using these bounds was 14.2% more accurate than the constrained Weibull, based on the Kolmogorov-Smirnov statistic. The truncated reverse Weibull fit dominant tree distributions 23.7% more accurately than the constrained Weibull, based on a mean absolute difference statistic. This work indicates that a blind spot may have developed in plantation growth modeling systems deploying constrained Weibull functions, and that left-truncation of unconstrained functions could substantially improve model accuracy for negatively skewed distributions.

scholarly journals A Hypothesis Test for the Goodness-of-Fit of the Marginal Distribution of a Time Series with Application to Stablecoin Data

2021 ◽  
Vol 5 (1) ◽  
pp. 10
Author(s):  
Mark Levene
Keyword(s):  
Time Series ◽  
Goodness Of Fit ◽  
Marginal Distribution ◽  
Hypothesis Test ◽  
Data Sets ◽  
Test Statistic ◽  
Sample Test ◽  
Kolmogorov Smirnov ◽  
Heavy Tailed ◽  
Jensen Shannon Divergence

A bootstrap-based hypothesis test of the goodness-of-fit for the marginal distribution of a time series is presented. Two metrics, the empirical survival Jensen–Shannon divergence (ESJS) and the Kolmogorov–Smirnov two-sample test statistic (KS2), are compared on four data sets—three stablecoin time series and a Bitcoin time series. We demonstrate that, after applying first-order differencing, all the data sets fit heavy-tailed α-stable distributions with 1<α<2 at the 95% confidence level. Moreover, ESJS is more powerful than KS2 on these data sets, since the widths of the derived confidence intervals for KS2 are, proportionately, much larger than those of ESJS.

Beyond the heuristic approach to Kolmogorov-Smirnov theorems

1982 ◽  
Vol 19 (A) ◽  
pp. 359-365 ◽  
Author(s):  
David Pollard
Keyword(s):  
Weak Convergence ◽  
Goodness Of Fit ◽  
Empirical Distribution ◽  
Distribution Functions ◽  
Heuristic Approach ◽  
Convergence Theory ◽  
Simple Method ◽  
Starting Point ◽  
Kolmogorov Smirnov ◽  
The Subject

The theory of weak convergence has developed into an extensive and useful, but technical, subject. One of its most important applications is in the study of empirical distribution functions: the explication of the asymptotic behavior of the Kolmogorov goodness-of-fit statistic is one of its greatest successes. In this article a simple method for understanding this aspect of the subject is sketched. The starting point is Doob's heuristic approach to the Kolmogorov-Smirnov theorems, and the rigorous justification of that approach offered by Donsker. The ideas can be carried over to other applications of weak convergence theory.

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