Estimating Dependence Between Lumber Strength Properties with Copula Models

We propose a copula-based approach to estimate the dependence between a pair of lumber strength properties that cannot be observed simultaneously, i.e., MOR and UTS. We also present a graphical method to evaluate whether a model can accurately represent the damage effect due to proof load. By fitting copula models, we conclude that there is a strong dependence between MOR and UTS even conditioning on other related properties such as MOE. We also find that the reflected Gumbel copula is a more suitable model for the lumber data compared with the Gaussian copula.