A 4-Variate Gompertz Type Diffusion Model: Computational Aspects and Applications

Abstract

This work focuses on modeling the growth dynamics for measurements of tree variables in a forest stand. Stochastic di erential equation (SDE) models allow us a better understanding of biological processes driving the dynamics of natural phenomena. In this study, we propose a system of the Gompertz type 4-variate xed e ect parameters SDEs to quantify the dynamics of tree size components distribution against the age in a forest stand with a sigmoid form trend for the mean value of tree size components. The new derived 4-variate probability density function and its marginal univariate, bivariate, trivariate and conditional univariate distributions are applied for the modeling of stand attributes such as the mean diameter, height, crown base height, crown width, volume and slenderness ratio. All parameters were estimated by the maximum likelihood procedure using real-life data set. The results are implemented in the symbolic algebra system MAPLE.