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A derivation for the Weibull distribution

Authors
Journal
Journal of Theoretical Biology
0022-5193
Publisher
Elsevier
Publication Date
Volume
81
Issue
1
Identifiers
DOI: 10.1016/0022-5193(79)90080-8
Disciplines
  • Biology
  • Ecology
  • Mathematics

Abstract

Abstract The Weibull distribution is increasingly finding application in the biological sciences, notably in forestry, where it has given good fits to tree-diameter frequency distribution. Interest among foresters is currently focused on improving the interpretation for the two parameters of this distribution, resulting in better understanding of forest stand growth. This paper presents a mathematical derivation of the Weibull distribution based on a generalization of the broken stick model used in ecology for species-abundance curves. This derivation suggests that the inverse of one parameter can be interpreted as an index of non-randomness and that the other parameter is inversely proportional to total frequency in an observed frequency distribution.

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