Comparison of beta, Johnson’s SB, Weibull and truncated Weibull functions for modeling the diameter distribution of forest stands in Catalonia (north-east of Spain)

The purpose of this study was to compare the beta, Johnson SB, Weibull and truncatedWeibull functions in describing the diameter distributions of forest stands in Catalonia. The data consisted of permanent sample plots from the Spanish National Forest Inventoryin Catalonia. The empirical data represent left- truncated distributions, as the smallest diameter measured in the field was 7.5 cm. A total of 1,242 plots were used to fit the functions and analyze their performance. The distribution functions were fitted to the diameter distributions of the number of stems (DDN) and stand basal area(DDG). The performance of the candidate functions was compared by means of their bias and RMSE for different diameter sums measuring the difference between the empirical and fitted distributions. The leftmost part (from 0 to 7.5 cm) of the non- truncatedfunctions was ignored in this analysis. Sensitivity analyses were conducted to check whether the results depended on the number of trees measuredin the stand, or the main species of the stand. The truncatedWeibull function for the diameter distribution of stand basal areaappeared to be in all cases the most accurate and consistent function. Generally, functions describing the distribution of stand basal areaperformed better than functions that described the distribution of the number of trees. Of the basal areadistributions, beta and Johnson’s SB were the second best and nearly equally good with each other. The order of precision of the tested functions was: truncatedWeibull for DDG, truncatedWeibull for DDN, Johnson’s SB for DDG, beta for DDG, beta for DDN and Weibull for DDG, Weibull for DDN, and Johnson’s SB for DDN.