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

Abstract

Modeling diameter distribution is a crucial aspect of forest management, requiring the selection of an appropriate probability density function or cumulative distribution function along with a fitting method. This study compared the suitability of eight probability density functions—A Charlier, beta, generalized beta, gamma, Gumbel, Johnson’s SB, and Weibull (two- and three-parameter)—fitted using both derivative methods (Moments) fitted in SAS/STATTM and optimization methods (MLE) fitted with the ‘optim’ function in R for diameter distribution estimation in forest stands. The A Charlier and Gumbel functions were used for the first time in this type of comparison. The data were derived from 167 permanent sample plots in an Atlantic forest (Quercus robur) and 59 temporary sample plots in tropical forests (Tectona grandis). Fit quality was assessed using various indices, including Kolmogorov–Smirnov, Cramér–von Mises, mean absolute error, bias, and mean squared error. The results indicated that Johnson’s SB function was more suitable for describing the diameter distribution of the stands. Johnson’s SB, three-parameter Weibull, and generalized beta consistently performed well across different fitting methods, while the fits produced by gamma, Gumbel, and two-parameter Weibull were of poor quality.