Bayesian Inference for Johnson's SB and Weibull distributions
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The four-parameter Johnson's SB (JSB) and three-parameter Weibull distributions have received much attention in the field of forestry for characterizing diameters at breast height (DBH). In this work, we suggest the Bayesian method for estimating parameters of the JBS distribution. The maximum likelihood approach uses iterative methods such as Newton-Raphson (NR) algorithm for maximizing the logarithm of the likelihood function. But there is no guarantee that the NR method converges. This fact that the NR method for estimating the parameters of the JSB distribution sometimes fails to converge was verified through simulation in this study. Further, it was shown that the Bayesian estimators presented in this work were robust with respect to the initial values and estimate the parameters of the JSB distribution efficiently. The performance of the JSB and three-parameter Weibull distributions was compared in a Bayesian paradigm when these models were fitted to DBH data of three plots that randomly selected from a study established in 107 plots of mixed-age ponderosa pine (Pinus ponderosa Dougl. ex Laws.) with scattered western junipers at the Malheur National Forest in south end of the Blue Mountains near Burns, Oregon, USA. Bayesian paradigm demonstrated that JBS was superior model than the three-parameter Weibull for characterizing the DBH distribution when these models were fitted to the DBH data of the three plots.
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