The bivariate power-normal distribution and the bivariate Johnson system bounded distribution in forestry, including height curves

A bivariate diameter and height distribution yields a unified model of a forest stand. The bivariate Johnson system bounded distribution and the bivariate power-normal distribution are explored. The power-normal distribution originates from the well-known Box-Cox transformation. As evaluated by the bivariate Kolmogorov-Smirnov distance, the bivariate power-normal distribution seems to be superior to the bivariate Johnson system bounded distribution. The conditional median height given the diameter is a possible height curve and is compared with a simple hyperbolic height curve. Evaluated by the height deviance, the hyperbolic function yields the best height prediction. A close second is the curve generated by a bivariate power-normal distribution. Johnson system bounded distributions suffer from the sigmoid shape of the association between height and diameter. The bivariate power-normal distribution is easy to estimate and has good numerical properties; therefore, it is a good candidate model for use in forest stands.