Evaluation of estimation methods for parameters of the probability functions in tree diameter distribution modeling

Abstract

One of the most commonly used statistical models for characterizing the variations of tree diameter at breast height is Weibull distribution. The usual approach for estimating parameters of a statistical model is the maximum likelihood estimation (likelihood method). Usually, this works based on iterative algorithms such as Newton-Raphson. However, the efficiency of the likelihood method is not guaranteed since there is no assurance that the Newton-Raphson method for maximizing the log-likelihood function will converge. In such cases, one option is to use a better estimation approach. In this study, several methods were compared for estimating the parameters of two- and three-parameter Weibull distributions. We applied ten methods for two-parameter and twelve methods for three-parameter cases. The data set was collected from natural beech dominated forest in northern Iran. The results demonstrated that among the estimators investigated for two-parameter Weibull distribution, the percentile method outperformed other competitors. In contrast, for three-parameter Weibull distribution, the trimmed L-moment (TL-moment) method and the modified method of moments (type I and type II) outperformed other competitors in terms of Cramer Von-Mises criterion and Kolmogorov-Smirnov criterion, respectively.

Keywords

• least square method
• method of maximum product spacings
• tl-moment
• weibull distribution
• weighted maximum likelihood estimator