An evaluation of various probability density functions for predicting diameter distributions in pure and mixed-species stands in Türkiye

Abstract

Aim of study: To assess the capabilities of some infrequently used probability density functions (PDFs) in modeling stand diameter distributions and compare their performance to that of typical PDFs. Area of study: The research was conducted in pure and mixed stands located in the OF Planning Unit of the Trabzon Forest Regional Directorate in Northern Türkiye. Material and methods: A set of 17,324 DBH measurements, originating from 608 sample plots located in stands of even-aged and pure and mixed stands, were obtained to represent various stand conditions such as site quality, age, and stand density in OF planning unit forests. In order to ensure a minimum of 30-40 trees in each sample plot, the plot sizes ranged from 0.04 to 0.08 hectares, depending on stand density. The parameters of PDFs include Weibull with 3P and 2P, Rice, Rayleigh, Normal, Nagakami, Lognormal with 2P and 3P, Lévy with 1p and 2P, Laplace, Kumaraswamy, Johnson’s SB, and Gamma were estimated using the maximum likelihood estimation (MLE) prediction procedure. Additionally, the goodness of fit test was combined with the Kolmogorov-Smirnov test (statistically at a 95% confidence interval). Main results: The Rayleigh distribution was the model that best explained the diameter distributions of pure and mixed forests in the OF Planning Unit (as Fit Index (FI) = 0.6743 and acceptance rate 96.4% based on the result of one sample Kolmogorov-Smirnov test). Research highlights: Less commonly used PDFs such as Rice, Nakagami, and Kumaraswamy-4P demonstrated superior predictive performance compared to some traditional distributions widely used in forestry, including Weibull-2P and -3P, Johnson’s SB, Normal, Gamma-3P, and Lognormal-3P.

Keywords

• Rayleigh distribution
• maximum likelihood estimation
• stand structures