The power-normal distribution: application to forest stands

Abstract

Foresters have long sought distribution functions capable of modeling a tree distribution that have good fit, yield flexible models, and are easy to use. The power-normal (PN) distribution originates from the inverse Box–Cox transformation and might be proven to fulfill these requirements. The PN has similarities with Johnson’s system-bounded (SB) distribution and can be seen as a contender. The PN 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 × 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. Johnson’s SB has four parameters and estimation is often susceptible to numerical problems when fitted by maximum likelihood estimation. Our results indicate that the performance of PN is superior to that of Johnson’s SB, as shown by the Kolmogorov–Smirnov statistic and visual inspection, particularly for fitting tree height distributions.