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Title: Asymptotically efficient estimation of a bivariate Gaussian–Weibull distribution and an introduction to the associated pseudotruncated Weibull

Source: USDA Forest Service, Forest Products Laboratory, Research Paper, FPL-RP- 666, 2012: 78 p.

Author(s)Verrill, Steve P.; Evans, James W.; Kretschmann, David E.; Hatfield, Cherilyn A.

Publication Year: 2012  View PDF »

Category: Research Papers
Associated Research Project(s):   FPL-4714-1A  FPL-4851-2A

Abstract: Two important wood properties are stiffness (modulus of elasticity or MOE) and bending strength (modulus of rupture or MOR). In the past, MOE has often been modeled as a Gaussian and MOR as a lognormal or a two- or three-parameter Weibull. It is well-known that MOE and MOR are positively correlated. To model the simultaneous behavior of MOE and MOR for the purposes of wood system reliability calculations, we introduce a bivariate Gaussian–Weibull distribution and the associated pseudo-truncated Weibull. We use asymptotically efficient likelihood methods to obtain an estimator of the parameter vector of the bivariate Gaussian--Weibull, and then obtain the asymptotic distribution of this estimator.

Keywords: Reliability; modulus of rupture; modulus of elasticity; one-step Newton estimator; Gaussian copula; normal distribution; Weibull distribution; likelihood methods

Publication Review Process: Non-Refereed (Other)

File size: 725 kb(s)

Date posted: 08/03/2012
RITS Product ID: 60557
Current FPL Scientists associated with this product (listed alphabetically)
Evans, James W.
Mathematical Statistician
Kretschmann, David E.
Research General Engineer
Verrill, Steve P.
Mathematical Statistician

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