Abstract
The four-parameter S
B distribution has seen widespread use in growth-and-yield modeling because it covers a broad spectrum of shapes, fitting both positively and negatively skewed data and bimodal configurations. Two recent parameter recovery schemes, an approach whereby characteristics of a statistical distribution are equated with attributes of a stand in order to solve for the parameters of the distribution, are described for the S
B. The first scheme permits recovery of the range and both shape parameters, but the location parameter must be a priori specified. The second scheme is an all-parameter recovery model. The details of the parameter recovery models, that is the system of equations with their concomitant constraints, are laid out. A solution technique for the constrained parameter recovery models that uses the Kuhn-Tucker conditions, the Lagrange function, and the Levenberg-Marquardt algorithm is briefly reviewed. Two Statistical Analysis System programs that implement the parameter recovery models, S
B Recovery 3parm and S
B Recovery 4parm, are listed and demonstrated with instructive examples.
Keywords
Basal area-size distribution,
constraint functions,
diameter distributions,
moments,
nonlinear programming problem,
restricted estimation
Citation
Parresol, Bernard R.; Fonseca, Teresa Fidalgo; Marques, Carlos Pacheco. 2010. Numerical details and SAS programs for parameter recovery of the S
B distribution. Gen. Tech. Rep. SRS–122. Asheville, NC: U.S. Department of Agriculture Forest Service, Southern Research Station. 27 p.