Evaluation of usefulness of selected functions for modeling distribution of breast height diameter in black alder stands (Alnus glutinosa (L.) Gaertn.)

We evaluated the usefulness of ten theoretical probability density functions for the approximation of the breast height diameter distributions in managed alder stands growing in the western part of the Sandomierz Basin (southern Poland). The study material consisted of measurement results for 22,530 alders obtained for 844 circular sample plots, established in 163 stands aged 6-89. In the area of particular stands, from 2 to 10 age-dependent circular sample plots sized 0.01-0.10 ha were systematically arranged. We evaluated the following theoretical probability distributions: normal (N), double normal (P-N), Johnson S-B (J), Weibull (W), beta (B), Burr (Bu), gamma (G), log-normal (L-N), log-logistic (L-L) and Birnbaum-Saunders (B-S). Additionally the usefulness of the W, B, Bu, G, L-N, L-L and B-S distributions with omitted location parameter was tested. The goodness-of-fit of each probability density function was assessed based on the Kolmogorov-Smirnov statistic, the root mean square error and ranks established on their basis. It was found that DBH distribution of majority stands is characterized by right-sided asymmetry and negative kurtosis. It was showed that the best distribution for the breast height diameter structure approximation of alder stands is the Johnson SB (J) distribution. To describe the frequency of thickness, normal (N) and log-logistic (L-L) distribution should not be used. Elimination of location parameter significantly affects usefulness of probability density functions to modeling empirical distributions of breast height diameter. Gamma and Burr distributions with omitted location parameter gave the best results in description the frequency of breast height diameter. In certain situations, these distributions can also be used to describe the structure of breast height diameter of alder stands.