A Two-Stage Fitting Method for Truncated Stem Diameter Distributions

Gregory Paradis 

Stem diameter distributions underpin growth projections, harvest scheduling, and carbon accounting, yet permanent sample plot inventories are routinely truncated by merchantability limits and maximum expected diameters. The accepted remedy is to fit truncated versions of the desired density, but those forms are seldom documented or supported in common software, so practitioners often default to biased complete-form fits. We revisit the truncated-diameter problem and introduce a two-stage weighted least-squares workflow that retains the familiar complete-form implementation while recovering the truncated solution. 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 Quebec, Canada, the approach matches truncated Weibull and gamma fits across 11 species-group / cover-type combinations, limiting the absolute AICc gap to 0.006. The companion repository provides the tallies, scripts, and notebooks required to regenerate every figure, table, and LaTeX artefact, supporting operational replication.