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A Two-Stage Fitting Method for Truncated Stem Diameter Distributions
1Department of Forest Resources Management, University of British Columbia, Vancouver, Canada.
Forest Science
|August 15, 2026
Summary
Forest inventory data often has missing values due to size limits. This study introduces a two-stage method to accurately estimate complete stem diameter distributions using existing software, improving forest planning.
Area of Science:
- Forestry science
- Quantitative ecology
- Statistical modeling
Background:
- Forest inventory data is frequently truncated by merchantability limits and diameter caps.
- Existing methods for handling truncated data are often not supported by common software, leading to biased estimations.
- Practitioners often default to complete-form fits, which can be inaccurate for truncated datasets.
Purpose of the Study:
- To introduce a novel two-stage weighted least-squares workflow to accurately estimate complete stem diameter distributions from truncated data.
- To provide a method that integrates seamlessly with familiar complete-form implementations.
- To improve the accuracy of forest inventory and planning by addressing data truncation biases.
Main Methods:
- A two-stage weighted least-squares approach was developed.
- Stage one estimates density parameters and a scaling factor.
- Stage two refines estimates by fixing the normalizer, yielding unbiased shape and scale parameters.
Main Results:
- The two-stage method accurately recovers truncated-fit accuracy, outperforming biased complete-form fits.
- Applied to Québec forest plots, the method showed strong performance across 32 species-group/cover-type combinations.
- The two-stage estimator yielded the lowest small-sample Akaike information criterion (AICc) in 25 out of 32 cases.
Conclusions:
- The proposed two-stage method offers a practical and accurate solution for analyzing truncated stem diameter data.
- This approach enhances the reliability of forest planning and inventory practices.
- The associated repository provides all necessary resources for reproducibility.
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