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Modeling the Basal Area-size Distribution of Forest Stands: A Compatible Approach

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This paper presents a methodology that allows diameter distributions to be conformably modeled by letting the probability density represent either tree frequency as in the classic case, or basal area. The key to relating the two forms of the probability density is shown to lie in weighted distribution theory. The motivation for the relationship lies in the quadratic relationship between diameter at breast height and basal area. The weighted distribution approach is shown to be compatible with current methods of calculating quantities such as basal area by diameter class, but in addition, affords the development of new equations useful in parameter recovery or similar modeling strategies. Relationships are developed for all of the major distributions found to have been useful in forestry for fitting diameter distribution models. Several stands to which the two- and three-parameter Weibull distributions have been fitted are also presented. For. Sci. 44(2):285-297.

Keywords: Diameter distributions; maximum likelihood; parameter recovery; weighted distributions

Document Type: Journal Article

Affiliations: Distinguished Professor and Director, Center for Statistical Ecology and Environment Statistics, Department of Statistics, The Pennsylvania State University, 421 Thomas Building, University Park, PA 16802-2112

Publication date: 1998-05-01

More about this publication?
  • Forest Science is a peer-reviewed journal publishing fundamental and applied research that explores all aspects of natural and social sciences as they apply to the function and management of the forested ecosystems of the world. Topics include silviculture, forest management, biometrics, economics, entomology & pathology, fire & fuels management, forest ecology, genetics & tree improvement, geospatial technologies, harvesting & utilization, landscape ecology, operations research, forest policy, physiology, recreation, social sciences, soils & hydrology, and wildlife management.
    Forest Science is published bimonthly in February, April, June, August, October, and December.

    2015 Impact Factor: 1.702
    Ranking: 16 of 66 in forestry

    Average time from submission to first decision: 62.5 days*
    June 1, 2016 to Feb. 28, 2017

    Also published by SAF:
    Journal of Forestry
    Other SAF Publications
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