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

Jose Javier Gorgoso-Varela,Alberto Rojo-Alboreca

doi:10.5424/fs/2014233-04939

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.

Highlights

Forest managers must respond to current demands and consider forests as multi-purpose sites
For Quercus robur L. stands, the most suitable methods were the Percentiles followed by Maximum Likelihood for the Weibull probably density function (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 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

Summary

Introduction

Forest managers must respond to current demands and consider forests as multi-purpose sites (in terms of carbon storage, landscape value, as recreational sites, etc.). For this purpose, they need tools to evaluate different management practices and their effects on stand structure. Diameter class models enable managers to predict stand growth and plan various uses, and they provide data about stand structure. Such models are used to estimate stand variables and their structure with a probably density function (PDF) or a cumulative distribution function (CDF), either of which is fitted to diameter at breast height distributions or individual tree volume. The scope of the present paper is limited to fitting distributions to data comparing distributions with different numbers of parameters

Objectives

Methods

Results