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A note on the relationship between the quadratic mean stand diameter and harmonic mean basal area under size-biased distribution theory

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This note seeks to extend the utility of size-biased distribution theory as applied to forestry through two relationships regarding the quadratic mean stand diameter. First, the quadratic mean stand diameter's relationship to the harmonic mean basal area for horizontal point sampling, which has been known algebraically from early on, is proved under size-biased distribution theory. Second, a new result, which may prove most valuable in viewing the graphical representation of assumed distributions, is also derived. The results are also shown to apply to the basal area – size distribution, providing a unique duality between the two means.

Cette note vise à élargir la portée de la théorie de la distribution diamétrale biaisée telle qu'elle est appliquée en foresterie par le biais de deux propriétés du diamètre moyen quadratique du peuplement. D'abord, la théorie est utilisée pour démontrer la relation qui existe entre le diamètre moyen quadratique du peuplement et la surface terrière moyenne harmonique dans le cas de l'échantillonnage horizontal par point; une relation dont la démonstration algébrique est connue depuis longtemps. Deuxièmement, un nouveau résultat qui peut s'avérer très utile pour représenter graphiquement des distributions présumées est également dérivé de la théorie. Ces résultats sont aussi applicables à la distribution de la surface terrière par rapport au diamètre établissant ainsi une dualité unique entre le diamètre moyen et la surface terrière moyenne.[Traduit par la Rédaction]

Document Type: Research Article

Publication date: August 1, 2003

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  • Published since 1971, this monthly journal features articles, reviews, notes and commentaries on all aspects of forest science, including biometrics and mensuration, conservation, disturbance, ecology, economics, entomology, fire, genetics, management, operations, pathology, physiology, policy, remote sensing, social science, soil, silviculture, wildlife and wood science, contributed by internationally respected scientists. It also publishes special issues dedicated to a topic of current interest.
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