Characterizing Diameter Distributions by the use of the Weibull Distribution

Rennolls, K.; Geary, D. N.; Rollinson, T. J. D.

doi:10.1093/forestry/58.1.57

Cited by 94 publications

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“…Furthermore, the use of the two-parameter model avoids having to predict the situation parameter a (a = 0 in this case), which is always complex and not very accurate (Ortega, 1989;Maltamo et al, 1995). The Pearson's correlation analysis revealed close linear correlation between the scale parameter b and the quadratic mean diameter (d g ), in accordance with Álvarez-González (1997) and García-Guëmes et al (2002) who obtained linear models for this relationship, with values of adjusted determination coefficient (R 2 adj ) close to 99%, higher than that obtained by Rennolls et al (1985) for Picea sitchensis stands.…”

supporting

confidence: 74%

“…The Weibull probability density function was first used for modelling diameter distributions of pure and even-aged stands (Bailey and Dell, 1973), and since then it has been used in many growth models based on diameter distributions because of its flexibility and simplicity (Rennolls et al, 1985;Maltamo et al, 1995;Kangas and Maltamo, 2000;Zhang et al, 2003;Liu et al, 2004).…”

Section: Introductionmentioning

confidence: 99%

“…In both models the values of adjusted determination coefficient (R 2 adj ) were high (0.89 and 0.63, respectively) considering that the prediction of this parameter is often not very accurate. Rennolls et al (1985) and Maltamo et al (1995) for example, only explained a small part of the total variability in the parameter (5% and a 31% respectively), in the first case with a parabolic model including the mean diameter, and in the second case, with a linear model including the quadratic mean diameter and the natural logarithm of the age. Palahí et al (2006a) developed parameter prediction models for Pinus sylvestris, Pinus nigra and Pinus halepensis in Catalonia using the truncated Weibull function.…”

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confidence: 99%

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Modelling diameter distributions of Betula alba L. stands in northwest Spain with the two-parameter Weibull function

et al. 2007

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The diameter distributions of 125 permanent plots installed in birch dominated (Betula alba L.) stands in Galicia were modelled with the two-parameter Weibull distribution. Four different fitting methods were used: that based on percentiles of the distribution, non linear regression, maximum likelihood and the method of moments. The most accurate fit was obtained with the non linear regression (NLR) approach, considering the following statistics in the comparison: bias, mean absolute error (MAE), mean square error (MSE) and number of plots rejected by the Kolmogoroff-Smirnoff (KS) test.The scale parameter (b) and the shape parameter (c) obtained with the most accurate method (non linear regression), were first modelled with simple linear models and then related to commonly measured prediction variables (quadratic mean diameter, dominant height and stand density) with the parameter prediction model (PPM). The parameters fitted with the method of moments were recovered with the parameter recovery model (PRM) from the first and the second moments of the distribution (mean diameter and variance, respectively). Results indicated that both methods were successful in predicting the diameter frequency distributions. The PRM was more accurate than the PPM method.Key words: diameter class model, two-parameter Weibull distribution, fitting methods, parameter modelling. ResumenModelización de las distribuciones diamétricas en masas de Betula alba L. en el noroeste de España con la función Weibull biparamétrica Las distribuciones diamétricas de 125 parcelas permanentes instaladas en masas puras de abedul (Betula alba L.) en Galicia fueron modelizadas con la distribución Weibull de dos parámetros. Se emplearon cuatro métodos de ajuste: basados en percentiles de la distribución, regresión no lineal, máxima verosimilitud y el método de los momentos. Los ajustes más precisos fueron obtenidos con regresión no lineal, considerando los siguientes estadísticos en la comparación de los resultados: sesgo, error medio absoluto, error medio cuadrático y número de parcelas rechazadas por el test de Kolmogoroff-Smirnoff.El parámetro de escala (b) y el parámetro de forma (c) obtenidos con el método más preciso (regresión no lineal), fueron relacionados con variables de masa de frecuente medición (diámetro medio cuadrático, altura dominante y densidad) mediante modelos lineales sencillos aplicando la metodología de predicción de parámetros. Los parámetros ajustados con el método de los momentos fueron recuperados con modelos de recuperación de parámetros a partir del primer y del segundo momento de la distribución (diámetro medio y varianza, respectivamente). Los resultados indicaron que ambos métodos fueron satisfactorios para predecir las distribuciones de frecuencias de diámetros. El mé-todo de recuperación de parámetros fue más preciso que el método de predicción de parámetros.Palabras clave: modelo de clases diamétricas, distribución Weibull biparamétrica, métodos de ajuste, modelización de parámetros.

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Section: Introductionmentioning

confidence: 99%

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confidence: 99%

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Modelling diameter distributions of Betula alba L. stands in northwest Spain with the two-parameter Weibull function

et al. 2007

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“…Así, el problema radica en la necesidad de predecir con precisión los parámetros de la FDP que determinan la distribución diamétrica en un momento específico del tiempo. Cuando la distribución diamétrica real de un rodal se conoce, existen varios (Rennolls, Geary, & Rollison, 1985); ii) the estimation based on different percentiles of the distribution (Bailey & Dell, 1973;Shiver, 1988); iii) the estimation obtained by nonlinear regression by using iterative procedures, and iv) methods based on values of specific moments of the diameter distribution (Shifley & Lentz, 1985). If the aim is to project the density function when the actual number of trees is not known in each diameter class, the methodologies to be used differ from the above and can be classified into one of the following two groups (Hyink & Moser, 1983): i ) parameter estimation methods, and ii) recovery parameter methods.…”

Section: Introductionmentioning

confidence: 99%

Caracterización de las estructuras diamétricas de los bosques naturales del noroeste de Durango, México

Corral-Rivas¹,

González²,

Corral-Rivas³

et al. 2015

Rev Cha Se Cie For y del Amb

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T he diameter distribution of 44 permanent plots (conifers and broadleaf trees) was modeled using the three-parameter Weibull and Johnson's S B probability density functions (PDFs) in Santiago Papasquiaro, Durango. Four different methods of fitting parameters were used: maximum likelihood (ML), moments (MM), non-linear regression by ordinary least squares (ONLS) and percentiles (MP). The best method of fitting parameters for conifers and broadleaf trees was the method of moments. In modeling the Weibull PDFs, it was assumed that the location parameter (e) corresponds to the minimum measurable diameter. The scale parameter (λ) was modeled using the method of prediction parameter (PPM) through a linear regression relating to the quadratic mean diameter and dominant height of the stand. Finally, the shape parameter (γ) was indirectly recovered by the method of moments through prediction of the average diameter of the stand. According to the Kolmogorov-Smirnov test (P= 0.05), 71 % of the plots for the group of conifers and 68 % of the plots for the group of broadleaf species come from a population that follows the fitting distribution function. ResumenL a distribución diamétrica de 44 parcelas permanentes (coníferas y latifoliadas) se modeló a través de las funciones de densidad de probabilidad (FDP) Weibull de tres parámetros y S B Johnson, en el municipio de Santiago Papasquiaro, Durango. Para ello, se emplearon cuatro métodos de ajuste de parámetros: máxima verosimilitud, momentos, regresión no lineal por mínimos cuadrados ordinarios y percentiles. El mejor método de ajuste para las especies de coníferas y latifoliadas fue el método de momentos. En el modelado de la FDP Weibull se asumió que el parámetro de localización (e) corresponde al diámetro mínimo inventariable de la distribución. El parámetro de escala (λ) se modeló con el procedimiento de predicción de parámetros a través de un modelo de regresión lineal simple que relaciona γ con el diámetro cuadrático medio y la altura dominante del rodal. Finalmente, el parámetro de forma (γ) fue recuperado indirectamente por el método de momentos a través de la predicción del diámetro medio del rodal. De acuerdo con la prueba de Kolmogorov-Smirnov (P = 0.05), 71 % de las parcelas del grupo de especies de coníferas y 68 % de las parcelas del grupo de latifoliadas provienen de una población que sigue la función de distribución ajustada. Palabras clave: Coníferas, latifoliadas, función Weibull, modelado diamétrico.

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“…A wide range of probability density functions have been used in forestry to model tree diameter distributions (e.g., log-normal: Bliss and Reinker 1964;gamma: Nelson 1964;Weibull: Bailey and Dell 1973;Rennolls et al, 1985;beta: Zohrer 1972;Li et al, 2002), although the three-parameter Weibull and the four-parameter beta and SB models are possibly the most frequently used. Mohammad Alizade et al, (2009) investigated the tree diameter at breast height in uneven-aged stands and fitting a statistical distribution to them.…”

Section: Introductionmentioning

confidence: 99%

Modeling Diameter Distribution of the Tropical Rainforest in Oban Forest Reserve

Igbinosa¹,

Ejakhe²

2014

JEE

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Diameter distribution model was developed for tropical rainforest of Oban Forest Reserve. Multistage sampling technique was adopted for the study. The sampling procedure was made up of primary, secondary and tertiary sampling units. A total of 808 trees were measured in 14 tertiary sample plots (40m x 50m). Tree outside bark diameter at breast height (dbh) data, were measured for tree species with dbh ≥ 10 cm within the tertiary sampling units. Data were analysed on several probability density function (pdf), then ranked based on Kolmogorov smirnov, Anderson darling and Chi-Square.

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Characterizing Diameter Distributions by the use of the Weibull Distribution

Cited by 94 publications

References 0 publications

Modelling diameter distributions of Betula alba L. stands in northwest Spain with the two-parameter Weibull function

Modelling diameter distributions of Betula alba L. stands in northwest Spain with the two-parameter Weibull function

Caracterización de las estructuras diamétricas de los bosques naturales del noroeste de Durango, México

Modeling Diameter Distribution of the Tropical Rainforest in Oban Forest Reserve

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