Comparison of Beta, Gamma Weibull Distributions for Characterising Tree Diameter in Oluwa Forest Reserve, Ondo State, Nigeria

Abstract

This study compared the accuracy of the Beta, 2-parameter Gamma (2P) and 3-parameter Weibull (3P) distributions, fitted with the method of moments, for characterising the tree diameter of the reserve. Comparison was based on the Kolmogorov-Smirnov statistic (K-S), bias, mean absolute error (MAE), and mean square error (MSE). Distributions with location parameter were fixed as the minimum inventoried diameter of each plot.  A total of eight (8) temporary sample plots (TSPs) of size 50m x 50m were laid in the natural stand of the reserve. Systematic line transect was used in the laying of the plots. All trees with DBH ? 10.0cm in the selected plots were enumerated, identified and measured. The results from the goodness-of-fit statistics revealed that the Weibull (3P) distribution performed slightly better than the Beta distribution used in this study. The mean values for the K-S, bias, MAE, and MSE of the Weibull distribution were 0.11449, 0.00015, 0.00847, and 0.00022, respectively; as such ranked best. The Gamma (2P) distribution provided the worst fit to the dataset, with relatively large values for the goodness-of-fit statistics. It fits for the entire plot were far from the reverse J-shaped of natural forests, which implies that the Gamma (2P) distribution is inappropriate for determining the structure of the natural stand.

Keywords: diameter characterisation, probability distribution, moments, natural forest