Use of Gumbel and Weibull functions to model extreme values of diameter distributions in forest standsReport as inadecuate

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1 Departamento de Biología de Organismos y Sistemas, Escuela Politécnica de Mieres, Universidad de Oviedo 2 Unidade de Xestión Forestal Sostible UXFS, Departamento de Enxeñaría Agroforestal, Escola Politécnica Superior, Campus Universitario, Universidade de Santiago de Compostela

Abstract : & 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 mini-mum 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 moments-based methods, proved more suitable than the Weibull distri-bution 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 de-scribing the distribution of extreme diameter values in forest stands in northwest Spain. This is the first exam-ple of the application of the Gumbel distribution in forest modelling.

Author: J. Javier Gorgoso-Varela - Alberto Rojo-Alboreca -



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