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

Publisher： Society of American Foresters

ISSN： 0015-749X

Source： Forest Science, Vol.48, Iss.1, 2002-02, pp. : 47-58

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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 S_BB 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 S_BB 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 S_BB across the 43 plots when the models are used in tree volume prediction. FOR. SCI. 48(1):47–58.