Evaluation of Methods to Predict Weibull Parameters for Characterizing Diameter Distributions

Compared to other distribution functions, the Weibull distribution has been more widely used in describing diameter distributions because of its flexibility and relative simplicity. Parameters of the Weibull distribution are generally predicted either by the parameter prediction method or by the parameter recovery method. The coefficients of the regression equations for predicting Weibull parameters, moments, or percentiles are often estimated by use of different approaches such as ordinary least squares (OLS), seemingly unrelated regression (SUR) or cumulative distribution function regression (CDFR). However, there is no strong rationale for preferring one method over the other. We developed and evaluated different methods of predicting parameters of Weibull distribution to characterize diameter distribution using data from the Southwide Seed Source Study.The SUR and the CDFR approaches were applied to ten different parameter prediction and parameter recovery methods. A modified CDFR approach was developed by modifying the CDFR technique such that the CDF is computed using information from diameter classes instead of individual trees as in the CDFR approach. These methods were evaluated based on four goodness-of-fit statistics (Anderson-Darling, Kolmogorov-Smirnov, negative Log-Likelihood, and Error Index). The CDFR approach provided better results than the SUR approach for all methods. The Modified CDFR approach consistently provided better results than the SUR approach, and was superior to the CDFR approach in all evaluation statistics but the Anderson-Darling statistic.