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A fit of a mixture of bivariate normals to lumber stiffness : strength data


Author:
S. P. Verrill, Frank Charles Owens 1971-, David E. Kretschmann, Rubin Shmulsky, and Forest Products Laboratory (U.S.)
Source:
USDA
Year:
2018
Subject:
Distribution (Probability theory), Lumber, Mechanical properties, Elastic properties, Fracture, Statistics, Simulation methods, Weibull distribution, and Gaussian distribution
Abstract:
It has been common practice to assume that a two-parameter Weibull probability distribution is suitable for modeling lumber strength properties. In a series of papers published from 2012 to 2018, Verrill et al. demonstrated theoretically and empirically that the modulus of rupture (MOR) distribution of a visual grade of lumber or of lumber that has been “binned” by modulus of elasticity (MOE) is not a two parameter Weibull. Instead, the tails of the MOR distribution are thinned via “pseudo-truncation.” The theoretical portion of Verrill et al.'s argument was based on the assumption of a bivariate normal--Weibull MOE--MOR distribution for the full (“mill run”) population of lumber. Verrill et al. felt that it was important to investigate this assumption. In a recent pair of papers, they reported results obtained from a sample of size 200 drawn from a mill run population. They found that normal, lognormal, three-parameter beta, and Weibull distributions did not fit the sample MOR distribution of these data. Instead, it appeared that the MOR data might be fit by a skew normal distribution or a mixture of two univariate normals. In this paper, we investigate whether the joint MOE--MOR data from Verrill et al.'s recent mill run study can be well modeled as a mixture of two bivariate normals.
Format:
1 online resource (23, [21] pages) : illustrations (some color).
Language:
English
Publisher:
United States Department of Agriculture, Forest Service, Forest Products Laboratory
Series:
Research paper
Collection:
USDA publications
Permanent URL:
https://purl.fdlp.gov/GPO/gpo117603