A comparison of estimation methods for fitting Weibull and Johnson’s SB functions to pedunculate oak (Quercus robur) and birch (Betula pubescens) stands in northwest Spain

Abstract

Aim of study: In this study we compared the accuracy of the Weibull and the Johnson’s SB functions for describing diameter distributions in pedunculate oak (Quercus robur L.) and birch (Betula pubescens Ehrh.) stands.Area of study: Galicia (Northwest Spain).Material and Methods: A total of 172 diameter distributions in pedunculate oak and 202 in birch stands were finally evaluated. We compared the accuracy of three commonly used estimation methods of the Weibull and four estimation methods of the Johnson’s SB functions for describing these diameter distributions.Main results. For Quercus robur L. stands, the most suitable methods were the Percentiles followed by Maximum Likelihood for the Weibull PDF and the method of Moments for the Johnson’s SB PDF. For Betula pubescens Ehrh. stands, the best fits obtained with the Percentiles and Maximum Likelihood methods were also superior to the method of Moments, whereas the Conditional Maximum Likelihood and method of Moments provided the best results for the Johnson’s SB PDF, depending on the statistic and the value of the location parameter considered.Research highlights: Both distributions were suitable. The results were better for pedunculate oak than for birch stands.Keywords: Knoebel and Burkhart; location parameter; percentiles; maximum likelihood; moments; mode.