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<p>Stem diameter distributions underpin forest planning and inventory practice worldwide, yet permanent sample plot inventories are routinely truncated by merchantability limits and diameter caps. Truncated densities are the standard remedy, but those forms are seldom documented or supported in common software, so practitioners default to biased complete-form fits. We introduce a two-stage weighted least-squares workflow that retains the familiar complete-form implementation while recovering truncated-fit accuracy. Stage one estimates a scaling factor alongside the density parameters; stage two freezes that normaliser to deliver unbiased shape and scale estimates. Applied to fixed-area plots from Québec, Canada, the two-stage estimator tracks truncated Weibull and gamma fits across 32 species-group/cover-type combinations (root-mean-square error between one-stage truncated and two-stage complete fits: <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(2\times 10^{-5}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>2</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>5</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation>–<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(3.7\times 10^{-2}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>3.7</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>2</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation>) and yields the lowest stage-2 AICc (small-sample Akaike information criterion) in 25 of 32 cases. The companion repository provides the tallies, scripts, and notebooks required to regenerate every figure, table, and LaTeX artefact.</p>

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A Two-Stage Fitting Method for Truncated Stem Diameter Distributions

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  • 发表日期：

    2026年6月15日

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  • Gregory E. Paradis

摘要

Stem diameter distributions underpin forest planning and inventory practice worldwide, yet permanent sample plot inventories are routinely truncated by merchantability limits and diameter caps. Truncated densities are the standard remedy, but those forms are seldom documented or supported in common software, so practitioners default to biased complete-form fits. We introduce a two-stage weighted least-squares workflow that retains the familiar complete-form implementation while recovering truncated-fit accuracy. Stage one estimates a scaling factor alongside the density parameters; stage two freezes that normaliser to deliver unbiased shape and scale estimates. Applied to fixed-area plots from Québec, Canada, the two-stage estimator tracks truncated Weibull and gamma fits across 32 species-group/cover-type combinations (root-mean-square error between one-stage truncated and two-stage complete fits: \(2\times 10^{-5}\) 2 × 10 - 5 – \(3.7\times 10^{-2}\) 3.7 × 10 - 2 ) and yields the lowest stage-2 AICc (small-sample Akaike information criterion) in 25 of 32 cases. The companion repository provides the tallies, scripts, and notebooks required to regenerate every figure, table, and LaTeX artefact.