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

The three-parameter Weibull density is commonly used to model the dist ribution of tree diameters in forest stands. We demonstrate, through l ikelihood profiles, that maximum likelihood estimation is often inappr opriate for data from young trees due to negative estimates of the loc ation parameter. We suggest a Bayesian model and fit it, using the Gib bs sampler, to three data sets. The latter model is easy to implement and guarantees a positive estimate for the location parameter. We illu strate some novel forms of model diagnostics, demonstrating that the B ayesian model is appropriate for two of the data sets, while it is dub ious for the third. A sampling-resampling method shows that the lack o f fit of the model for the latter data set is due to the likelihood, a nd not the prior specification.