Age-varying bivariate distribution models for growth prediction

摘要

Height-diameter models are classically analyzed by fixed or mixed linear and non-linear regression models. In order to possess the among-plot variability, we propose stochastic differential equations that are deduced from the standard deterministic dynamic ordinary differential equations by adding the process variability to the growth dynamic. The advantage of the stochastic differential equation framework is that it analyzes a residual variability, corresponding to measurements error, and an individual variability to represent heterogeneity between subjects. An analysis of 1575 Scots pine (Pjnus sylvestris) trees provided the data for this study. The results are implemented in the symbolic computational language MAPLE.