An approach to modeling the joint distribution of tree diameter and height data

ABSTRACT

Advantages of the application of bivariate distribution models to forest management cannot be overemphasized. However, there are quite a number of flexible statistical distributions not yet evaluated in their bivariate domains. Therefore, in this article, we evaluated the bivariate forms of some probability distribution models used in quantitative forestry. Six bivariate distributions were assessed: Burr XII (Burr XII-2), Dagum (Dagum-2), Kumaraswamy (Kum-2), the new Logit-Logistic-Dagum (LLD-2) distribution, Logit-Logistic (LL-2), and the much used Johnson’s S_BB. All models were constructed using the Plackett’s method except for the S_BB distribution. Appropriate constraints were imposed on the boundary parameters of the bivariate distributions using fractions derived from the Gumbel distribution. Models were fitted with maximum likelihood to the joint distribution of diameter and height data of Eucalyptus camaldulensis Dehn from 90 sample plots. Model assessment was based on negative log-likelihood (-ΛΛ), Corrected Akaike Information Criterion (AICc), Bayesian Information Criterion (BIC) and Hannan-Quinn Criterion (HQC). The result showed that the Johnson’s S_BB had the overall best performance. Their ranking order was: S_BB > LLD-2 > Burr XII-2 > Dagum-2 > LL-2 > Kum-2. These models can be used to simulate timber harvesting regime.

KEYWORDS:

• Bivariatelogit-logistic-dagum
• bivariate logit-logistic
• Johnson’s S_BB
• bivariate kumaraswamy
• bivariate burr distributions