Goodness-of-fit tests and model selection procedures for diameter distribution models

The process of developing diameter distribution yield models based on probability distributions involves selecting a family of probability distributions, developing a methodology for estimating the distribution parameters, and validating the final selected model. Standard goodness-of-fit tests have been widely used at various stages of this process, often in an ad hoc manner. Goodness-of-fit tests are reviewed and formalized and problems associated with applications to diameter distribution models are discussed. The effect of correlations between tree diameters on a plot and the effect of using multistage techniques to estimate the parameters of the probability distribution are investigated. Results from a simulation of the entire fitting process suggest that, in many situations, use of goodness-of-fit tests may be inappropriate. Other testing and selection procedures that may be more appropriate than goodness-of-fit are reviewed. As an alternative to goodness-of-fit tests, an error index is proposed for use in selecting and validating models. The error index is used in conjuction with the fitting process simulation to investigate the effect of the fitting technique and the characteristics of the fitting data on final model selection.