Estimation and applications of size-biased distributions in forestry

Size-biased distributions arise naturally in several contexts in forestry and ecology. Simple power relationships (e.g. basal area and diameter at breast height) between variables are one such area of interest arising from a modelling perspective. Another, probability proportional to size (PPS) sampling, is found in the most widely used methods for sampling standing or dead and fallen material in the forest. Often it is desirable or necessary to estimate a parametric probability density model based on size-biased data. Traditional equal probability methods may not be appropriate, or may be less efficient in such circumstances, and estimation is better conducted utilizing size-biased theory. This chapter surveys some of the possible uses of size-biased distribution theory in forestry and related fields.