A finite mixture distribution approach for characterizing tree diameter distributions by natural social class in pure even-aged Scots pine stands in Poland

The overall diameter distribution of an even-aged stand can be treated as a compound of distributions of trees belonging to various classes. The presented study shows the applicability of a finite mixture distribution approach for describing diameter structure of such classes on an example of pure, even-aged Scots pine stands. We performed our study under an assumption that all starting values for parameter fitting should be available as a result of a routine forest inventory. When the parameters of the mixture are fitted to the unimodal distributions without any constraints, this approach often fails. This is because components of such distributions strongly overlap, and the fact of overlapping falsifies information about individual components. For a mixture forming a unimodal distribution, due to difficulties in fitting, it is necessary to use functions that exhibit certain skewness and are relatively flexible, such as lognormal or gamma. There is also a need for providing better start information, keeping certain parameters fixed, or using a multi-stage fitting. Despite possible problems with fitting parameters to the strongly overlapping distributions, this approach shows much potential in practical applications in silviculture and growth and yield modeling.