Evaluating optimal percentile pairs for a Weibull-based diameter distribution in European black pine stands

Abstract

Understanding the diameter distribution of forest stands is essential for sustainable forest management, as it offers critical information about stand structure, growth dynamics, and potential timber yield. This study aims to identify the optimal percentile pairs and the most suitable modeling approaches for characterizing the diameter distribution of European black pine (Pinus nigra Arn.) stands in Türkiye via a three-parameter Weibull distribution. A Percentile-based recovery method was utilized for recovering the Weibull parameters. Eight percentile pairs (10th and 90th, 25th and 50th, 25th and 75th, 31st and 63rd, 31st and 95th, 50th and 75th, 50th and 95th, and 63rd and 75th percentiles) were evaluated through four different estimation approaches: ordinary least squares (OLS), seemingly unrelated regression (SUR), cumulative distribution function regression (CDFR), and stand table regression (STR). The results indicate that the percentile pair 31st and 63rd, when combined with CDFR, demonstrated the highest overall performance. In contrast, the 50th and 75th pairs combined with OLS and SUR demonstrated a lower performance. Among the estimation approaches, CDFR consistently achieves the best parameter recovery across most percentile pairs, whereas OLS and SUR often result in less accurate estimations. These findings suggest that specific percentile pairs, particularly 31st and 63rd, in combination with CDFR, offer superior characterization of diameters in black pine stands. This study provides a comprehensive evaluation of different percentile pairs and estimation approaches, contributing valuable information for forest management and modeling practices.