Modeling Diameter Distributions with Six Probability Density Functions in Pinus halepensis Mill. Plantations Using Low-Density Airborne Laser Scanning Data in Aragón (Northeast Spain)

Abstract

The diameter distributions of trees in 50 temporary sample plots (TSPs) established in Pinus halepensis Mill. stands were recovered from LiDAR metrics by using six probability density functions (PDFs): the Weibull (2P and 3P), Johnson’s SB, beta, generalized beta and gamma-2P functions. The parameters were recovered from the first and the second moments of the distributions (mean and variance, respectively) by using parameter recovery models (PRM). Linear models were used to predict both moments from LiDAR data. In recovering the functions, the location parameters of the distributions were predetermined as the minimum diameter inventoried, and scale parameters were established as the maximum diameters predicted from LiDAR metrics. The Kolmogorov–Smirnov (KS) statistic (Dn), number of acceptances by the KS test, the Cramér von Misses (W2) statistic, bias and mean square error (MSE) were used to evaluate the goodness of fits. The fits for the six recovered functions were compared with the fits to all measured data from 58 TSPs (LiDAR metrics could only be extracted from 50 of the plots). In the fitting phase, the location parameters were fixed at a suitable value determined according to the forestry literature (0.75·dmin). The linear models used to recover the two moments of the distributions and the maximum diameters determined from LiDAR data were accurate, with R2 values of 0.750, 0.724 and 0.873 for dg, dmed and dmax. Reasonable results were obtained with all six recovered functions. The goodness-of-fit statistics indicated that the beta function was the most accurate, followed by the generalized beta function. The Weibull-3P function provided the poorest fits and the Weibull-2P and Johnson’s SB also yielded poor fits to the data.

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

“…but less so in Tasmanian blue gum (Eucalyptus globulus Labill) and Monterrey pine (Pinus radiata D. Don) stands. Gorgoso-Varela et al [24] modeled the diameter distributions with six PDFs-beta, generalized beta, Gamma-2P, Johnson's SB, and Weibull (two-and three-parameter)-in Pinus halepensis Mill. plantations using low-density Airborne Laser Scanning data in Aragón (northeast Spain).…”

“…The method of Moments for the two-parameter gamma function is computed by the following expressions [24]:…”

“…It is characterized by the location parameter ε, the scale parameter λ, and the shape parameters γ and δ (asymmetry and kurtosis parameters, respectively). The method of Moments used by Cosenza et al [28] and Gorgoso-Varela et al [24] is computed as follows:…”

Developing Weibull-based diameter distributions for the major coniferous species in Heilongjiang Province, China

“…The KS statistic evaluates the fitting performance of the models by measuring the maximum absolute distance between the given empirical CDF and the predicted CDF (Gorgoso-Varela et al 2021). The KS statistics for plot i was calculated (Massey 1951) as follows (Eqs.…”