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    The four-parameter SB 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 SB. 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, SB Recovery 3parm and SB Recovery 4parm, are listed and demonstrated with instructive examples.

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    Parresol, Bernard R.; Fonseca, Teresa Fidalgo; Marques, Carlos Pacheco. 2010. Numerical details and SAS programs for parameter recovery of the SB distribution. Gen. Tech. Rep. SRS–122. Asheville, NC: U.S. Department of Agriculture Forest Service, Southern Research Station. 27 p.


    Basal area-size distribution, constraint functions, diameter distributions, moments, nonlinear programming problem, restricted estimation

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