Evaluation of estimation methods for fitting the three-parameter Weibull distribution to European beech forests

Abstract

Biogeosciences and Forestry Biogeosciences and Forestry Evaluation of estimation methods for fitting the three-parameter Weibull distribution to European beech forests Živa Bončina (1-2) , Vasilije Trifković (1) , Christian Rosset (3) , Matija Klopčič (1) We evaluated three estimation methods for fitting the three-parameter Weibull distribution to even-aged European beech (Fagus sylvatica) forests by using experimental tree diameter data collected in 3709 sample plots (500 m 2 each). The maximum likelihood estimation method (MLE), the method of moments (MOM) and the method of modified moments type 1 (MM1) were applied for fitting the Weibull function. The goodness-of-fit of stand parameters (total tree number, stand basal area, dominant stand diameter and mean quadratic diameter) was tested by MAE and RMSE, and the probability and cumulative density functions of trees per 5 cm diameter classes were additionally tested by the Kolmogorov-Smirnov test and compared with Kolmogorov-Smirnov's D statistic. All three methods are suitable for estimating stand parameters based on the fitted Weibull function. Fitting the diameter distribution per 5 cm diameter classes at the plot level was less accurate due to the low number of trees or irregular diameter distribution of trees. The MM1 method was found to be the most suitable for fitting the three-parameter Weibull distribution to beech forests represented by data derived from small plots.

A Comparison of Probability Density Functions Fitted by Moments and Maximum Likelihood Estimation Methods Used for Diameter Distribution Estimation

“…The Weibull function has been fitted by derivative methods such as Moments, percentiles, and optimization to mixed spruce-fir stands [20] and tropical and Atlantic forests [6]. Recently, the same methods were used for the Weibull function to characterize the diameter distribution of European beech (Fagus sylvatica L.) [21]. The gamma function has been fitted by Moments [9] and optimization [6].…”