The Gompertz type stochastic growth law and a tree diameter distribution

The study presents a comprehensive stand-level model for the tree diameter distribution. A Gompertz type stochastic logistic growth law is used for describing diameter distribution. Using the Gompertz type stochastic law of tree diameter growth, the age and height dependent probability density function of diameter distribution is obtained. The mean age-diameter, height-diameter growth trends and their variances for the Gompertz type stochastic differential equation are derived. The expected tree diameter distribution is predicted by using the Fokker-Plank equation and stand measurements. The estimates of parameters are performed by the L-1 distance procedure. The Weibull, and negative exponential distributions are selected to study their performance to the observations. To evaluate the goodness-of-fit, the absolute discrepancy, Kolmogorov-Smirnov, and Reynolds error index statistics are adapted. In addition, for estimating the goodness-of-fit, the Chi-squared test, pseudo-residuals, and Shapiro-Francia statistic are arranged, and the normal quantile plot is described. To model the diameter distribution, as an illustrative experience, a real data set from repeated measurements on permanent sample plots of pine stands in Dubrava forest district is used. The results are implemented in the symbolic computational language MAPLE.