Height-diameter curve estimation and prediction with vasicek model

Abstract

In this paper we use a stochastic differential equation to describe the evolution of the height of an individual tree. Height-diameter modelling is most often performed using non-linear regression models based on ordinary differential equations. In this study, new model of tree height dynamics are examined with the Vasicek type stochastic differential equation and fixed-effects parameters. The parameters are estimated by considering discrete sampling of the diameter and height and by using maximum likelihood procedure. New developed model was employed to compare predicted values with observed values of a height. Performance statistics for the height-diameter equations included statistical indexes, Shapiro-Wilk test and normal probability plot. We use the data of tropical Atlantic moist forest trees in south eastern Brazil to validate our modelling technique. Results indicate that our model is able to capture the behaviour of tree height quite accurately. All results were implemented in a symbolic algebra system MAPLE.