A comparison of estimation methods for fitting Weibull, Johnson’s SB and beta functions to Pinus pinaster, Pinus radiate and Pinus sylvestris stands in northwest Spain

J J Gorgoso,A Cámara-Obregón,U Diéguez-Aranda,A Rojo

doi:10.5424/fs/2012213-02736

J J Gorgoso, A Cámara-Obregón + Show 2 more

Open Access

https://doi.org/10.5424/fs/2012213-02736

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Abstract

The purpose of this study was to compare the accuracy of the Weibull, Johnson’s SB and beta distributions, fitted with some of the most usual methods and with different fixed values for the location parameters, for describing diameter distributions in even-aged stands of Pinus pinaster, Pinus radiata and Pinus sylvestris in northwest Spain. A total of 155 permanent plots in Pinus sylvestris stands throughout Galicia, 183 plots in Pinus pinaster stands throughout Galicia and Asturias and 325 plots in Pinus radiata stands in both regions were measured to describe the diameter distributions. Parameters of the Weibull function were estimated by Moments and Maximum Likelihood approaches, those of Johnson’s SB function by Conditional Maximum Likelihood and by Knoebel and Burhart’s method, and those of the beta function with the method based on the moments of the distribution. The beta and the Johnson’s SB functions were slightly superior to Weibull function for Pinus pinaster stands; the Johnson’s SB and beta functions were more accurate in the best fits for Pinus radiata stands, and the best results of the Weibull and the Johnson’s SB functions were slightly superior to beta function for Pinus sylvestris stands. However, the three functions are suitable for this stands with an appropriate value of the location parameter and estimation of parameters method.

Highlights

Maritime pine (Pinus pinaster Ait.), Monterrey pine
Pinus pinaster stands throughout Galicia and Asturias (101 plots in Galicia and 82 plots in Asturias) and 325 permanent plots in Pinus radiata stands in both regions (212 plots in Galicia and 113 in Asturias) were measured to describe the diameter distributions
The bias and mean square error (MSE) for the fits with the three functions in each diameter class followed similar trends (Fig. 1), the Weibull function fitted by the moments approach and fixing the situation parameter as 50% of minimum observed diameter provided the poorest results for the smallest diameter classes

Summary

Introduction

Maritime pine (Pinus pinaster Ait.), Monterrey pine Don) and Scots pine (Pinus sylvestris L.) stands are important natural resources in northwest Spain (in the autonomous regions of Galicia and Asturias). These species are mainly present in pure stands, but sometimes in mixed stands. The climate in this area is the most suitable for timber production in Spain, with an annual harvest volume of almost 50% of the total for the entire country. The mean annual harvest volume for the period 19952002 in Galicia was 2,261,305 m3 from Pinus pinaster stands (39% of the total for Galicia), 597,606 m3 (10.5% of the total) from Pinus radiata stands, and 59,303 m3 from Pinus sylvestris stands (1% of the total) (Dans et al, 2005). In Asturias, the total annual harvest volume for the three species in the period 2007 and 2008 was 110,854 m3 (17% of the total for Asturias) (SADEI 2010)

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