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 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.

AN ALTERNATIVE TEST FOR UNIFORMITY

2009 ◽  
Vol 16 (04) ◽  
pp. 343-356 ◽  
Author(s):  
ZHENMIN CHEN ◽  
CHUNMIAO YE
Keyword(s):  
Probability Distribution ◽  
Goodness Of Fit ◽  
Integral Transformation ◽  
Test Statistic ◽  
Goodness Of Fit Test ◽  
Underlying Distribution ◽  
Goodness Of Fit Tests ◽  
Kolmogorov Smirnov ◽  
Alternative Test ◽  
Smirnov Test

Improving power of goodness-of-fit tests is an important research topic in statistics. The goal of the goodness-of-fit test is to check whether the underlying probability distribution, from which a sample is drawn, differs from a hypothesized distribution. Numerous research papers have been published in this area. It has been shown that the power of the existing goodness-of-fit tests in the literature is unsatisfactory when the alternative distributions are of V-shape or when the sample sizes are small. This motivates the development of more powerful test statistics. In this research, a new test statistic is proposed. The result can be used to test whether the underlying probability distribution differs from a uniform distribution. By applying the probability integral transformation, the proposed test statistic can be used to check whether the underlying distribution differs from any hypothesized distribution. The performance of the method proposed in this research is compared with the Kolmogorov–Smirnov test, which is a widely adopted statistical test in the literature. It has been shown that the test proposed in this proposal is more powerful than the Kolmogorov–Smirnov test in some cases.

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.

Prediction of Haemoglobin Level by Some Probability Distribution

2020 ◽  
Vol 9 (1) ◽  
pp. 84-88
Author(s):  
Govinda Prasad Dhungana ◽  
Laxmi Prasad Sapkota
Keyword(s):  
Probability Distribution ◽  
Normal Distribution ◽  
Goodness Of Fit ◽  
Continuous Variable ◽  
Hemoglobin Level ◽  
Chi Square ◽  
Chi Square Test ◽  
Log Normal ◽  
Two Parameters ◽  
Best Fit

 Hemoglobin level is a continuous variable. So, it follows some theoretical probability distribution Normal, Log-normal, Gamma and Weibull distribution having two parameters. There is low variation in observed and expected frequency of Normal distribution in bar diagram. Similarly, calculated value of chi-square test (goodness of fit) is observed which is lower in Normal distribution. Furthermore, plot of PDFof Normal distribution covers larger area of histogram than all of other distribution. Hence Normal distribution is the best fit to predict the hemoglobin level in future.

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 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 DESEMPENHO DE FUNÇÕES DE DENSIDADE PROBABILÍSTICAS PARA DESCREVER A DISTRIBUIÇÃO DIAMÉTRICA DE Pinus taeda, NA REGIÃO DE CAÇADOR, SC

FLORESTA ◽  
2012 ◽  
Vol 42 (4) ◽  
pp. 741 ◽  
Author(s):  
Saulo Jorge Téo ◽  
Júlio César Bianchi ◽  
Adriano Peloso ◽  
Paulo Roberto Nava ◽  
Alan Marcon ◽  
...  
Keyword(s):  
Probability Density ◽  
Pinus Taeda ◽  
Diameter Distribution ◽  
Maximum Diameter ◽  
Density Functions ◽  
Horizontal Structure ◽  
Kolmogorov Smirnov ◽  
Pinus Taeda L ◽  
Site Classes ◽  
Smirnov Test

ResumoO objetivo deste trabalho foi analisar as funções de densidade probabilísticas (FDP) Normal, Ln-Normal, Sb de Johnson, Weibull 3P, Gamma, Beta e Weber, para descrever as mudanças na estrutura diamétrica de povoamentos de Pinus taeda L., na região de Caçador (SC), em diferentes idades e classes de sítio. O processamento dos dados foi realizado por meio da ferramenta Solver, do software MS Excel 2010, a qual utiliza o algoritmo linear de gradiente reduzido generalizado (GRG) na interação dos parâmetros. Verificou-se que a FDP Sb de Johnson e Weibull 3 P apresentaram os melhores desempenhos. Para a avaliação da aderência das FDP, é recomendada a utilização das estatísticas R2, R2aj, syx e syx%, além do teste de Kolmogorov-Smirnov, em todos os casos, especialmente quando houver número de observações superior a 5.000. Geralmente, houve um aumento da amplitude dos valores dos diâmetros e um achatamento da distribuição diamétrica com o avanço da idade e com a melhora da produtividade do sítio. Com o progresso da idade, há um aumento dos valores do diâmetro máximo e do diâmetro modal das distribuições, para as classes de sítio de maior produtividade, porém o mesmo não ocorre para o sítio menos produtivo. AbstractPerformance of probability density functions in order to describe diameter distribution of Pinus taeda, in the region of Caçador, SC. This research aims to analyze probability of density functions (pdf) Normal, Ln-Normal, Johnson Sb, 3 P Weibull, Gamma, Beta and Weber in order to describe  diameter changes in Pinus taeda L. plantations structure, in the region of Caçador - SC, Brazil, at different age and site classes. The data processing was carried out by Solver tool of the software MSExcel2010, using the linear algorithm of generalized reduced gradient (GRG) for interaction of parameters. As result, Johnson Sb and 3PWeibull presented the best performances. For the pdf adherence evaluation, it was recommended the employment of R2, R2aj, syx e syx% statistics, besides the Kolmogorov-Smirnov test, in any situation, specially, when there is more than 5,000 observations. Generally, there was an increasing in the range of diameter values and a flatness of diameter distribution at advancing age and improvement of the site productivity. At age advancing, there was an increasing of maximum diameter and modal diameter values of distributions, for the higher productivity site classes, on the other hand, the same did not occur for the low productivity site class.Keywords: Horizontal structure; Kolmogorov-Smirnov test; probability density function; forestry site.

scholarly journals A Cautionary Note on the Use of the Kolmogorov–Smirnov Test for Normality

2007 ◽  
Vol 135 (3) ◽  
pp. 1151-1157 ◽  
Author(s):  
Dag J. Steinskog ◽  
Dag B. Tjøstheim ◽  
Nils G. Kvamstø
Keyword(s):  
Goodness Of Fit ◽  
Small Sample ◽  
Power Comparison ◽  
Goodness Of Fit Test ◽  
Kolmogorov Smirnov ◽  
The Mean ◽  
Small Sample Problem ◽  
Tests For Normality ◽  
Test For Normality ◽  
Smirnov Test

Abstract The Kolmogorov–Smirnov goodness-of-fit test is used in many applications for testing normality in climate research. This note shows that the test usually leads to systematic and drastic errors. When the mean and the standard deviation are estimated, it is much too conservative in the sense that its p values are strongly biased upward. One may think that this is a small sample problem, but it is not. There is a correction of the Kolmogorov–Smirnov test by Lilliefors, which is in fact sometimes confused with the original Kolmogorov–Smirnov test. Both the Jarque–Bera and the Shapiro–Wilk tests for normality are good alternatives to the Kolmogorov–Smirnov test. A power comparison of eight different tests has been undertaken, favoring the Jarque–Bera and the Shapiro–Wilk tests. The Jarque–Bera and the Kolmogorov–Smirnov tests are also applied to a monthly mean dataset of geopotential height at 500 hPa. The two tests give very different results and illustrate the danger of using the Kolmogorov–Smirnov test.

scholarly journals Probabilistic Assessment of Degree of Bending in Tubular X-Joints of Offshore Structures Subjected to Bending Loads

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Hamid Ahmadi ◽  
Amirreza Ghaffari
Keyword(s):  
Probability Distribution ◽  
Goodness Of Fit ◽  
Accurate Determination ◽  
Offshore Structures ◽  
Fatigue Reliability ◽  
Distribution Models ◽  
Estimated Parameters ◽  
Jacket Structures ◽  
Kolmogorov Smirnov ◽  
Bending Loads

Fatigue life of tubular joints in offshore structures is significantly influenced by the degree of bending (DoB). The DoB exhibits considerable scatter calling for greater emphasis in accurate determination of its governing probability distribution which is a key input for the fatigue reliability analysis of a tubular joint. Although the tubular X-joints are commonly found in offshore jacket structures, as far as the authors are aware, no comprehensive research has been carried out on the probability distribution of the DoB in tubular X-joints. In the present paper, results of parametric equations available for the calculation of the DoB have been used to develop probability distribution models for the DoB in the chord member of tubular X-joints subjected to four types of bending loads. Based on a parametric study, a set of samples was prepared and density histograms were generated for these samples using Freedman-Diaconis method. Twelve different probability density functions (PDFs) were fitted to these histograms. In each case, Kolmogorov-Smirnov test was used to evaluate the goodness of fit. Finally, after substituting the values of estimated parameters for each distribution, a set of fully defined PDFs have been proposed for the DoB in tubular X-joints subjected to bending loads.

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.

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