SB distribution’s accuracy to represent the diameter distribution of Pinus taeda, through five fitting methods

Scolforo, José Roberto Soares; Tabai, Fernando César Vitti; Macedo, Renato Luís Grisi; Acerbí, Fausto Weimar; Assis, Adriana Leandra de

doi:10.1016/s0378-1127(02)00183-4

Cited by 28 publications

(18 citation statements)

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“…Finally, the KB method was slightly inferior to MMJ and CML in terms of D n , but values of MAE and MSE were similar to those obtained by the CML when c = 10%. Different values of the location parameter in Johnson's S B function have been compared in several studies (Knoebel & Burkhart, 1991;Zhou & McTague, 1996;Zhang et al, 2003;Scolforo et al, 2003;Parresol, 2003;Palahí et al, 2007;Fonseca et al, 2009;Gorgoso et al, 2012).…”

Section: Resultsmentioning

confidence: 99%

A comparison of estimation methods for fitting Weibull and Johnson’s SB functions to pedunculate oak (Quercus robur) and birch (Betula pubescens) stands in northwest Spain

Gorgoso-Varela¹,

Alboreca

2014

For. syst.

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Aim of study: In this study we compared the accuracy of the Weibull and the Johnson’s SB functions for describing diameter distributions in pedunculate oak (Quercus robur L.) and birch (Betula pubescens Ehrh.) stands.Area of study: Galicia (Northwest Spain).Material and Methods: A total of 172 diameter distributions in pedunculate oak and 202 in birch stands were finally evaluated. We compared the accuracy of three commonly used estimation methods of the Weibull and four estimation methods of the Johnson’s SB functions for describing these diameter distributions.Main results. For Quercus robur L. stands, the most suitable methods were the Percentiles followed by Maximum Likelihood for the Weibull PDF and the method of Moments for the Johnson’s SB PDF. For Betula pubescens Ehrh. stands, the best fits obtained with the Percentiles and Maximum Likelihood methods were also superior to the method of Moments, whereas the Conditional Maximum Likelihood and method of Moments provided the best results for the Johnson’s SB PDF, depending on the statistic and the value of the location parameter considered.Research highlights: Both distributions were suitable. The results were better for pedunculate oak than for birch stands.Keywords: Knoebel and Burkhart; location parameter; percentiles; maximum likelihood; moments; mode.

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Section: Resultsmentioning

confidence: 99%

A comparison of estimation methods for fitting Weibull and Johnson’s SB functions to pedunculate oak (Quercus robur) and birch (Betula pubescens) stands in northwest Spain

Gorgoso-Varela¹,

Alboreca

2014

For. syst.

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“…Predetermination of the location parameters of the PDFs or the CDFs used in studies involving diameter class models usually depends on the minimum diameter of the distributions (Zanakis 1979;Hawkins et al 1988;Knoebel and Burkhart 1991;Zhang et al 2003;Scolforo et al 2003;Parresol 2003;Cao 2004, Liu et al 2004, Fonseca et al 2009Gorgoso et al 2012), and a suitable value of the location parameter is an important factor in the final accuracy of the models. In distributions including high minimum diameter values, a low value of the location parameter is probably not appropriate.…”

Section: Discussionmentioning

confidence: 99%

“…However, the optimum extension of the upper limit may be more closely related to the trend in the frequency of trees in the highest diameter classes than the value of the maximum diameter of the distribution. Maximum diameter has also been used to determine the scale parameter in the Johnson's S B PDF (Knoebel and Burkhart 1991;Gorgoso et al 2012), and it has also been used to estimate the scale parameter as the range of the distributions (Schreuder and Hafley 1977;Scolforo et al 2003). Maximum diameters also are used in some generalized height-diameter models, sometimes as one of the independent variables (Lenhart 1968;Amateis et al 1995).…”

Section: Discussionmentioning

confidence: 99%

“…This avoids the need to use complicated and laborious algorithms as used for example by Scolforo et al (2003) and Gorgoso et al (2012).…”

Section: Practical Applicationmentioning

confidence: 99%

“…Furthermore, the maximum diameter of the distributions and the upper limit of the highest diameter class, which depend on the maximum diameter, are usually used as the upper boundary in four-parameter distributions such as the beta function (Zöhrer 1969(Zöhrer , 1970Loetsch et al 1973;Gorgoso-Varela et al 2008). This value is also used as a scale parameter, in the Johnson's S B four-parameter distribution (Gorgoso et al 2012) or in combination with the minimum diameter to calculate the range used as the scale parameter (Schreuder and Hafley 1977;Scolforo et al 2003). The maximum diameter is also considered as an independent variable in some generalized height-diameter models (Lenhart 1968;Amateis et al 1995).…”

Section: Introductionmentioning

confidence: 99%

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Use of Gumbel and Weibull functions to model extreme values of diameter distributions in forest stands

Gorgoso-Varela

Alboreca

2014

Annals of Forest Science

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& Context Families of the Gumbel (type I), Fréchet (type II) and Weibull (type III) distributions can be combined in the generalized extreme value (GEV) family of distributions. Maximum and minimum values of diameters in forest stands can be used in forest modelling, mainly to define parameters of the functions used in diameter class models as well as in some practical cases, such as modelling maximum diameters for sawing and processing purposes. & Aims The purpose of this study was to examine and compare two extreme value distribution functions (the Gumbel and the Weibull functions) in modelling the distribution of the minimum and the maximum values of representative sets of tree diameter samples. Both of these functions were applied to the lower and upper values of the diameter distributions of the main forest species in northwest Spain: Quercus robur L., Betula pubescens Ehrh., Pinus radiata D. Don, Pinus pinaster Ait. and Pinus sylvestris L. & Methods Parameters of the Gumbel function were estimated using the mode and the moments of the distributions, and parameters of the Weibull function were estimated using the moments method.& Results In general, the Weibull distribution was the most suitable model for describing the maximum diameters. The mode method of the Gumbel yielded the best results for minimum diameters of birch and Monterrey pine. The Gumbel distribution, fitted by either the mode-or momentsbased methods, proved more suitable than the Weibull distribution for describing the minimum diameters in maritime pine and Scots pine stands. & Conclusion In some cases, better results were obtained with the Gumbel than the Weibull distribution for describing the distribution of extreme diameter values in forest stands in northwest Spain. This is the first example of the application of the Gumbel distribution in forest modelling.

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Diameter-Distribution Models for Even-Aged Stands

Burkhart

Tomé²

2012

Modeling Forest Trees and Stands

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SB distribution’s accuracy to represent the diameter distribution of Pinus taeda, through five fitting methods

Cited by 28 publications

References 5 publications

A comparison of estimation methods for fitting Weibull and Johnson’s SB functions to pedunculate oak (Quercus robur) and birch (Betula pubescens) stands in northwest Spain

A comparison of estimation methods for fitting Weibull and Johnson’s SB functions to pedunculate oak (Quercus robur) and birch (Betula pubescens) stands in northwest Spain

Use of Gumbel and Weibull functions to model extreme values of diameter distributions in forest stands

Diameter-Distribution Models for Even-Aged Stands

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