The purpose of this study was to compare the beta, Johnson SB, Weibull and truncated Weibull functions in describing the diameter
distributions of forest stands in Catalonia. The data consisted of permanent sample plots from the Spanish National Forest
Inventory in 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 (DD
N) and stand basal area (DD
G). 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-truncated functions
was ignored in this analysis. Sensitivity analyses were conducted to check whether the results depended on the number of trees
measured in the stand, or the main species of the stand. The truncated Weibull function for the diameter distribution of stand
basal area appeared to be in all cases the most accurate and consistent function. Generally, functions describing the distribution
of stand basal area performed better than functions that described the distribution of the number of trees. Of the basal area
distributions, 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: truncated Weibull for DD
G, truncated Weibull for DD
N, Johnson’s SB for DD
G, beta for DD
G, beta for DD
N and Weibull for DD
G, Weibull for DD
N, and Johnson’s SB for DD
N.
Keywords Distribution functions - Probability density functions - Stand structure
Communicated by Hans Pretzsch.