Modeling diameter distribution is a crucial aspect of forest management, requiring the selection of an appropriate probability density function or cumulative distribution function along with a fitting method. This study compared the suitability of eight probability density functions—A Charlier, beta, generalized beta, gamma, Gumbel, Johnson’s SB, and Weibull (two- and three-parameter)—fitted using both derivative methods (Moments) fitted in SAS/STAT^TM and optimization methods (MLE) fitted with the ‘optim’ function in R for diameter distribution estimation in forest stands. The A Charlier and Gumbel functions were used for the first time in this type of comparison. The data were derived from 167 permanent sample plots in an Atlantic forest (Quercus robur) and 59 temporary sample plots in tropical forests (Tectona grandis). Fit quality was assessed using various indices, including Kolmogorov–Smirnov, Cramér–von Mises, mean absolute error, bias, and mean squared error. The results indicated that Johnson’s SB function was more suitable for describing the diameter distribution of the stands. Johnson’s SB, three-parameter Weibull, and generalized beta consistently performed well across different fitting methods, while the fits produced by gamma, Gumbel, and two-parameter Weibull were of poor quality.

Eucalyptus ( Eucalyptus camaldulensis Dehnh.) is an important exotic species in northern Nigeria commonly used for poles and timber. Sustainable management of this resource would require quantifying its volume. Stem taper equations are one of the main and most efficient methods for estimating stem volume to any merchantable limit of a species. There is currently no taper equation for Eucalyptus species in Nigeria. Therefore, this study developed taper equations for E. camaldulensis in northern Nigeria. Data for this study were obtained from a private plantation in Jalingo Local Government Area, Taraba State, Nigeria. 68 trees were felled and sectioned into 1-m bolt across the stem to a merchantable limit of 5 cm, which were used as the fitting dataset. An additional 22 trees were felled and used to validate the taper equations for stem volume estimation. Seven taper equations were initially fitted to the dataset using nonlinear least squares. The best taper equation was then refitted using a nonlinear mixed-effects approach and calibrated using diameters of one to five sections from the butt end. The taper equations were numerically integrated to obtain the stem volume, which was compared with empirical volume equations. The result shows that the Kozak (Can J For Res 27(5): 619–629. 10.1139/x97-011, 1997) equation, which included eight parameters, provided the best fit for predicting section diameters for under and over bark. The mixed-effects taper equation (NLME-TE) explained most stem diameter variations in the fitting dataset (pseudo- R ² : 0.986–0.987; RMSE: 0.547–0.578 cm) without substantial residual trends. The validation showed that the prediction accuracy of the integrated NLME-TE improved as the number of sectional diameter measurements increased, with at least a 35% reduction in volume estimate error. For practical implementation, two calibration sectional diameter measurements taken from the butt end per tree are recommended. This approach would reduce measurement effort and cost while improving model performance.

Modelling diameter distribution is an integral part of forest management. It requires the use of a suitable probability density function or cumulative distribution function with the appropriate fitting method. In this study, we compared the suitability of eight probability density functions fitted by derivative and optimization methods used for diameter distribution estimation of forest stands. The derivation and optimization were used on A Charlier, beta, generalized beta, gamma, Gumbel, Johnson’s SB, and Weibull (2 and 3-parameter). We used data from 167 permanent sample plots from Atlantic forest (Quercus robur) and 59 temporary sample plots from tropical forests (Tectona grandis). The quality of the fits was evaluated with different indices such as Kolmogorov–Smirnov, Cramer-von Mises, mean absolute error, bias and mean squared error. The results showed Johnson’s SB function was more suitable for describing the diameter distribution of the stands. Johnson’s SB, 3-parameter Weibull and generalized beta had consistent performance regardless of the fitting methods. The quality of fits produced by gamma, Gumbel and 2-parameter Weibull was poor.