Describing Maritime Pine Diameter Distributions with Johnson's SB Distribution Using a New All-Parameter Recovery Approach

Abstract

Abstract Forest growth and yield models that describe the heterogeneity of a stand by implicitly defining size classes are valuable tools for sustainable forest management. In stand-level growth and yield models, often stand tables representing numbers of trees by diameter class are projected through the use of probability density functions (PDFs). Theoretical knowledge shows and empirical studies corroborate that the four-parameter Johnson's SB PDF provides greater generality in fitting diameter distributions than many of the commonly applied PDFs in forestry, such as the beta, gamma, and Weibull PDFs. Distinct parameter estimation methods are available for the Johnson's SB distribution. However, few studies have been conducted that estimate the Johnson's SB PDF using a parameter recovery approach. Also, for those studies that have used a parameter recovery approach, often one (i.e., the location) or two (i.e., the location and the range) of the four parameters are assumed to be known. In this article, we present a parameter recovery approach to recover all four parameters of the Johnson's SB PDF for diameter distributions from stand variables. The location, range, and shape parameters are recovered from the median and the first three noncentral moments of the diameter distribution. The first two of these noncentral moments correspond to the average and quadratic mean diameter. The third moment is interpreted as the product of the mean diameter for the diameter distribution based on basal area, rather than stems per ha, and the squared quadratic mean diameter. The proposed methodology is demonstrated for maritime pine (Pinus pinaster Ait.) stands in Portugal.