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The direct parameter prediction method (PPM), moment-based parameter recovery method (PRM), and percentile-based parameter recovery method (PCT) for estimating the parameters of the three-parameter Weibull probability density function were evaluated for their applicability in predicting the diameter distribution of unthinned black spruce (Picea mariana (Mill.) B.S.P.) plantations. Employing diameter frequency data derived from 267 permanent sample plots situated throughout central Canada, fit (n = 214) and validation (n = 53) data sets were created. Using stepwise regression analyses in combination with seemingly unrelated regression techniques, the three methods were calibrated using commonly measured prediction variables (stand age, dominant height, site index, and stand density). Results indicated that, although all three methods were successful in predicting the diameter frequency distributions within the sample stands, the PCT was superior in terms of prediction error. Specifically, the PCT had the lowest mean error index (80.98), followed by the PRM (82.73) and the PPM (83.98). Consequently, among the three methods assessed, the PCT was considered the most suitable for describing unimodal diameter distributions via the three-parameter Weibull probability density function within unthinned black spruce plantations.

ABSTRACT:Weibull distribution was used to fit tree diameter data collected from 86 sample plots located in Chinese pine stand in Beijing. To estimate the Weibull distribution parameters, three methods [namely maximum likelihood estimation method (MLE), method of moment (MOM) and least-squares regression method (LSM)] were compared and evaluated on the basis of the mean square error (MSE) and sample size. For these sample plots, the moment method was superior for estimating the parameters of Weibull distribution for tree diameter distribution.