Application of extreme value distribution for assigning optimum fractions to distributions with boundary parameters: an eucalyptus plantations case study

Abstract

The search for an optimum value to constrain boundary parameters in distribution models can be (and is) laborious and time-consuming. The accuracy of a distribution fit depends on the predetermined values of the boundary parameters. In this study, we applied the extreme value distributions derived from the generalized extreme value (GEV) in assigning the optimum constant to a distribution with boundary parameters. GEV subfamily (type 1), Gumbel’s distribution, was used to generate constant values which were used as a fraction of the minimum and maximum diameter and height data. The effectiveness of these values was established using five distribution models: logit-logistic (LL), Burr XII, Dagum, Kumaraswamy, and Johnson’s SB distributions. The distributions were fitted with maximum accuracy to the diameter and height data collected on 90 Eucalyptus camaldulensis Dehn sample plots. Model assessment was based on negative log-likelihood (-ΛΛ), Kolmogorov-Smirnov (K-S), Cramér-von Mises (W2), Reynold’s error index (EI), and mean square error (MSE). The result showed that the performance of the distributions was improved, especially for the height distribution, compared to other constant values. Gumbel’s distribution can be applied whenever (where) a boundary constraint is to be imposed on the location and scale parameters of the distribution models.

Keywords

• generalized extreme value
• Gumbel
• Kumaraswamy
• logit-logistic
• Burr XII
• Dagum
• Johnson SB