Recovering Parameters of Johnson's SB Distribution

  • Authors: Parresol, Bernard R.
  • Publication Year: 2003
  • Publication Series: Research Paper (RP)
  • Source: Res. Pap. SRS-31. Asheville, NC: U.S. Department of Agriculture, Forest Service, Southern Research Station. 9 p.


A new parameter recovery model for Johnson's SB distribution is developed. This latest alternative approach permits recovery of the range and both shape parameters. Previous models recovered only the two shape parameters. Also, a simple procedure for estimating the distribution minimum from sample values is presented. The new methodology employs the median and the first and second moments of the distribution. The methodology is demonstrated by modeling diameter distributions of unthinned loblolly pine plantations. Compatible equations for projecting per-hectare values of number of trees and basal area from initial stand conditions are presented, as well as equations for predicting median diameter, mean diameter, and the location parameter. Given estimates of these five stand attributes, the range and the two shape parameters of the SB distribution can be recovered. The 2 goodness-of-fit test rejected 56 cases out of 527 for conformance to an SB distribution. Though the SB distribution is very flexible in terms of distribution shape, about 10 percent of the loblolly plantation observations did not follow this distribution. Nonetheless, deviation analysis showed reasonable results, with 77 percent of the variation explained in current and projected distributions (numbers of trees by 2.5-cm diameter class). Overall, the recovered SB distributions provided good approximations of the observed diameter distributions.

  • Citation: Parresol, Bernard R. 2003. Recovering Parameters of Johnson''s SB Distribution. Res. Pap. SRS-31. Asheville, NC: U.S. Department of Agriculture, Forest Service, Southern Research Station. 9 p.
  • Keywords: Diameter distributions, kurtosis, Newton-Raphson method, moments, parameter recovery model, percentiles, Pinus taeda, skewness
  • Posted Date: April 1, 1980
  • Modified Date: August 22, 2006
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