|
Abstract:
|
Quantification of lumber properties is complex, and, due to the uniqueness of any particular piece of lumber, it is an inexact science. Further, it involves several measurable characteristics, two of the most common of which are Modulus of Elasticity (MOE) and Modulus of Rupture (MOR). These two characteristics tend to be related, and for lumber of a specific category (species, size, grade, etc.), MOE and MOR admit a bivariate dataset. Modeling this dataset has been a long-term endeavor. In the present work, we propose a 6-parameter conditionally-specified scaled bivariate beta (BBCSS) model which permits simple interpretation of its parameters in the context of MOE and MOR. Because MOE is measurable through non-destructive testing while only destructive testing can reveal MOR, MOE is often used as a predictor for MOR. The BBCSS model lends itself particularly well to this scenario. The fitness of the BBCSS model is compared to other models that have been proposed, and it provides similar fits to MOE/MOR data, but in some cases it has disadvantages. Both maximum likelihood and Bayesian methods of parameter estimation will be exhibited, and examples will be presented.
|
