The Power-Normal Distribution: Application to forest stands.

Abstract

The Power-Normal distribution (PN) originates from the inverse Box-Cox transformation and is used in this study to fit the frequency distributions of tree diameter and height. PN is flexible in describing different shapes of observed distributions as indicated by the certain areas in the skewness x kurtosis shape plane. The estimation of the parameters using maximum likelihood is straightforward and the resulting numerical properties are desirable. The shapes achieved by PN are very diverse, even though only three parameters are used. In forestry, Johnson’s System Bounded distribution (SB) has been widely used to fit tree diameter distributions, but it is often susceptible to numerical problems when fitted by maximum likelihood estimation. Our results indicate that the performance of PN is superior to Johnson’s SB, as shown by the Kolmogorov-Smirnov statistic and visual inspection, particularly for fitting the tree height distributions.