Modeling extreme values for height distributions in Pinus pinaster, Pinus radiata and Eucalyptus globulus stands in northwestern Spain

Abstract

Methods of estimating extreme height values can be used in forest modeling to improve fits to the marginal distribution of heights in the following bivariate diameter-height models: the SBB Johnson’s distribution, the bivariate beta (GDB-2) distribution, the bivariate Logit-Logistic (LL-2) distribution and the power-normal (PN) distribution. Some applications to LiDAR derived data are also possible, e.g., for error calibration. Practical applications in forest management may also be considered, e.g., for pruning. In probability theory and statistics, the generalized extreme value (GEV) distribution, also known as the Fisher-Tippett distribution, is a family of continuous probability distributions that combine the Gumbel, Fréchet and Weibull distributions. This study compared the three distributions for fitting extreme values of tree heights (maximum and minimum heights), which were measured in 185 permanent research plots in Pinus pinaster Ait. stands, 97 research plots in Pinus radiata D. Don stands, and 128 research plots in Eucalyptus globulus Labill. Most of the eucalyptus stands were measured three times giving a total of 304 measurements. All plots are located in northwestern Spain. The Bias, Mean Absolute Error (MAE) and Mean Square Error (MSE) of the mean relative frequency of trees were used to evaluate the goodness-of-fit of the different functions, as well as the Kolmogorov-Smirnov statistic Dn. The Gumbel and the Weibull cumulative distribution functions (CDFs) proved suitable for describing extreme values of height distributions of the above-mentioned tree species in northwestern Spain. The Fréchet distribution was only used to model maximum values and yielded the poorest results in all cases.