Some Bivariate Distributions for Modeling the Strength Properties of Lumber

摘要

Accurate modeling of the joint stochastic nature of the strength properties of211u001edimension lumber is essential to the determination of reliability-based safety 211u001efactors. This report reviews the major techniques for obtaining bivariate 211u001edistributions and then discusses bivariate distribution whose marginal 211u001edistributions suggest they might be useful for modeling the joint distribution of 211u001etwo strength properties. Finally, the authors pick a bivariate Weibull 211u001edistribution and show that they can write its likelihood function under a proof 211u001eloading scheme, offering the possibility that it can be used to model the joint 211u001edistribution of two properties that must each be measured using a destructive 211u001etest.