Asymptotically Efficient Estimation of a Bivariate Gaussian-Weibull Distribution and an Introduction to the Associated Pseudo-Truncated Weibull

• Activity Number: 419
• Type: Contributed
• Date/Time: Tuesday, July 31, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Steve Verrill*+ and James Evans and David Kretschmann and Cherilyn Hatfield
• Companies: USDA Forest Products Laboratory and USDA Forest Products Laboratory and USDA Forest Products Laboratory and USDA Forest Products Laboratory
• Keywords: reliabilty ; Gaussian copula ; one-step Newton estimator ; square root n consistent estimator ; modulus of rupture ; modulus of elasticity

Abstract

Motivated by wood product reliability issues, we define a bivariate Gaussian-Weibull, obtain asymptotically efficient estimates of its parameters, establish their asymptotic normality, discuss simulations that investigated the small sample properties of these estimators, and describe a web-based program that fits the distribution and obtains both asymptotic and simulation-based confidence bounds on its parameters. We also introduce the related pseudo-truncated Weibull distribution. This distribution arises when wood stiffness and wood strength have a bivariate Gaussian-Weibull distribution, and (as in "machine stress rating") wood is binned based on its stiffness.