A Weighted Fitting Approach for Diameter Distributions from Horizontal Point Sampling

Horizontal point sampling (HPS) produces size-biased tallies that cannot be fit directly with standard probability distributions without distorting diameter distribution estimates. Previous work resolves this by deriving bespoke size-biased probability density functions (PDFs) for each assumed distribution. We revisit the problem and formalise a weighted non-linear least squares approach that fits standard-form PDFs to expanded HPS stand tables while preserving the statistical equivalence with the size-biased formulation. The new pipeline leverages contemporary open-source software, is fully reproducible, and includes accompanying code that regenerates all figures and tables. Computational experiments on permanent sample plot data from Quebec demonstrate that the weighted method matches the reference approach to machine precision across Weibull and Gamma distributions. The manuscript and companion software provide a turnkey solution for practitioners who require stable, transparent, and replicable HPS diameter distribution fitting.