BAYESIAN-ESTIMATION FOR THE 3-PARAMETER WEIBULL DISTRIBUTION WITH TREE DIAMETER DATA

The three-parameter Weibull density is commonly used to model the distribution of tree diameters in forest stands. We demonstrate, through likelihood profiles, that maximum likelihood estimation is often inappropriate for data from young trees due to negative estimates of the location parameter. We suggest a Bayesian model and fit it, using the Gibbs sampler, to three data sets. The latter model is easy to implement and guarantees a positive estimate for the location parameter. We illustrate some novel forms of model diagnostics, demonstrating that the Bayesian model is appropriate for two of the data sets, while it is dubious for the third. A sampling-resampling method shows that the lack of fit of the model for the latter data set is due to the likelihood, and not the prior specification.