A Blind Spot in the Use of the Weibull Function for Modeling Diameter Distributions. Issue 2 (15th December 2020)

• Record Type: Journal Article
• Authors: Goodwin, Adrian Norman
• Is Part Of: Forest science. Volume 67:Issue 2(2021)
• Page Start: 125
• Page End: 134
• Publication Date: 2020-12-15
• Subjects: Weibull -- reverse Weibull -- truncated distributions -- parameter recovery method -- method of moments; Forests and forestry -- Periodicals; Forest management -- Periodicals; Forest policy -- United States -- Periodicals; Forest management; Forest policy; Forests and forestry; United States; Electronic journals; Periodicals; 634.9
• DOI: 10.1093/forsci/fxaa042
• Languages: English
• ISSNs: 0015-749X

Abstract

Abstract: Diameter distribution models based on probability density functions are integral to many forest growth and yield systems, where they are used to estimate product volumes within diameter classes. The three-parameter Weibull function with a constrained nonnegative lower bound is commonly used because of its flexibility and ease of fitting. This study compared Weibull and reverse Weibull functions with and without a lower bound constraint and left-hand truncation, across three large unthinned plantation cohorts in which 81% of plots had negatively skewed diameter distributions. Near-optimal lower bounds for the unconstrained Weibull function were negative for negatively skewed data, and the left-truncated Weibull using these bounds was 14.2% more accurate than the constrained Weibull, based on the Kolmogorov-Smirnov statistic. The truncated reverse Weibull fit dominant tree distributions 23.7% more accurately than the constrained Weibull, based on a mean absolute difference statistic. This work indicates that a blind spot may have developed in plantation growth modeling systems deploying constrained Weibull functions, and that left-truncation of unconstrained functions could substantially improve model accuracy for negatively skewed distributions.