ABSTRACT
Tree size can be described with different variables, such as tree diameter, height, volume, or crown width. Based on the standard probability theory, the chapter discusses approaches that can be used in describing and prediction of the marginal distribution of diameters in an area of interest. Similar presentation has not been published before. The chapter starts by discussing the use of a sample of tree diameters, where alternative approaches for smoothing are the kernel method and fitting an assumed distribution model to the data. Estimation based on maximum likelihood is suggested, even though other widely used methods are presented as well. Alternative models to describe unimodal and multimodal size distribution are discussed. Mathematics of tree size distributions is presented in the context of (weighted) continuous univariate and bivariate distribution theory. Examples about scaling the distribution to stand level are given using various stand level characteristics, and methods to recover diameter distribution and height-diameter curve based on known stand characteristics are presented. A statistical model for tree diameters within a forest stand and in a population of forest stands are formulated their use is demonstrated. A total of 33 examples illustrate the concepts and their use with real-life data sets.
