Modeling the Joint Distribution of Tree Diameters and Heights by Bivariate Generalized Beta Distribution

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Abstract:

A bivariate generalized beta distribution (GBD-2) is fit to the joint frequency distribution of tree diameters and heights of 43 Douglas-fir (Pseudotsuga menziesii var. glauca [Beissn.] Franco) plots in Idaho. The model fitting and performance are compared with the Johnson's SBB distribution using goodness-of-fit χ2 tests for the marginal distributions of diameters and heights, a bivariate goodness-of-fit test for the joint distribution of the two variables, and model predictions of tree heights and volumes. We found that the GBD-2 is more flexible and successful than the Johnson's SBB in describing both marginal and joint distributions of tree diameters and heights. On average, the relative bias (%) from the GBD-2 is three times smaller than that from the Johnson's SBB across the 43 plots when the models are used in tree volume prediction. FOR. SCI. 48(1):47–58.

Keywords: Generalized beta distribution; Johnson's SBB distribution; bivariate generalized beta distribution; environmental management; forest; forest management; forest resources; forestry; forestry research; forestry science; goodness-of-fit test; natural resource management; natural resources

Document Type: Miscellaneous

Affiliations: 1: Research Assistant Faculty of Forestry, State University of New York, College of Environmental Science and Forestry, One Forestry Drive, Syracuse, NY, 13210, Phone: (315) 471-8763 fali@syr.edu 2: Associate Professor Faculty of Forestry, State University of New York, College of Environmental Science and Forestry, One Forestry Drive, Syracuse, NY, 13210, Phone: (315) 470-6558, Fax: (315) 470-6535 lizhang@syr.edu 3: Faculty of Forestry, State University of New York, College of Environmental Science and Forestry, One Forestry Drive, Syracuse, NY, 13210, Phone: (315) 470-6569 cjdavis@syr.edu

Publication date: February 1, 2002

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