Applications and comparison of six methods for predicting parameters of the Weibull function in unthinned Picea glauca plantations

Abstract

The objectives of this study were (1) to compare six methods for predicting parameters of the Weibull probability density function (PDF) for diameter at breast height (dbh) distribution in the unthinned white spruce plantations in eastern Canada with respect to their applicability, and (2) to evaluate their predictive abilities in terms of error index (EI) and Kolmogorov–Smirnov (K-S) statistic. The reasons for undertaking this study were (1) there are no available models for the dbh distributions of the studied species and (2) to determine the best method for projecting dbh distributions of white spruce plantations. A total of 113 sample plots which consisted of the commonly measured stand-level variables [stand age (A), site index at 25-year base age (SI), average height of dominant and co-dominant trees (H _d), and stand density (SD)] and associated diameter frequency distributions were used in this study. Of all the six prediction methods, the moment-based and percentile-based parameter recovery approach (PRM and PCT), maximum likelihood estimation regression (MLER), cumulative distribution function regression (CDFR) and parameter prediction method (PPM) were able to be applied for adequately modeling the diameter frequency distributions for the data sets used in this study. The moment-percentile estimation hybrid method (HYBM) performed the poorest. PCT was most highly recommended as it had the consistently lowest EI and K-S statistic values for both fit and validation data sets. Therefore, the dbh distributions for white spruce plantations could be predicted at a point over time using the established methods here, especially the PCT method, from the stand variables (A, SI, H _d, SD).

Keywords:

• Parameter recovery method
• probability density function
• Weibull-based
• white spruce plantation

Acknowledgements

We would like to thank the Canadian Wood Fibre Centre of Natural Resources Canada for its financial support to this study. The data were collected and provided by the Ministère des Ressources naturelles et de la Faune du Québec.