Potential of the S<sub>B</sub> and S<sub>BB</sub> Distributions For Describing Mechanical Properties of Lumber

Authors

  • R. G. Pearson

Keywords:

Frequency distribution, lognormal distribution, Weibull distribution, lumber, mechanical properties, S<sub>B</sub> distribution, S<sub>BB</sub> distribution

Abstract

The SB distribution can fit a much wider range of shapes of frequency distributions than the log-normal and Weibull, or even the beta, distributions. Maximum likelihood estimates of the four parameters can be obtained.

A bivariate distribution between correlated variables A and B, e.g. modulus of rupture and modulus of elasticity, is readily calculated if an SB distribution is fitted to each variable, the only additional information needed being the value of the correlation coefficient between A and B. This distribution, known as the SBB distribution, is based on a transformation of the original values into normal deviates and so its properties can be determined from normal distribution theory. The conditional distribution of variable A for a given value of B is itself an SB distribution, the form of which may vary with the value of B to fit the test distribution of the A-values.

The SBB distribution offers a possible means of obtaining a probabilistic relationship between the various strength properties of lumber such as modulus of rupture and maximum tensile strength. Means of estimating the correlation coefficient between different strength properties are suggested and the effect of error in the estimate of the correlation coefficient is discussed.

References

Doyle, D. V., and L. J. Markwardt. 1966. Properties of southern pine in relation to strength grading of dimension lumber. U.S. Forest Service Research Paper FPL-64.nHafley, W. L., and H. T. Schreuder. 1977. Statistical distributions for fitting diameter and height data in even-aged stands. Can. J. For. Res. 7(3):481-487.nJohnson, N. L. 1949a. Systems of frequency curves generated by means of translation. Biometrika 36:149-176.nJohnson, N. L. 1949b. Bivariate distributions based on simple translation systems. Biometrika 36:297-304.nLeicester, R. L. 1979. Division of Building Research, Commonwealth Scientific and Industrial Research Organization, Australia. Private communication.nSchreuder, H. T., and W. L. Hafley. 1977. A useful bivariate distribution for describing stand structure of tree heights and diameters. Biometrics 33(3):471-478.nWarren, W. G. 1973. Estimation of the exclusion limit for dimension lumber. Proc. Meeting Division V, IUFRO, South Africa, September and October 1973. Vol. 2:1148-1154.nWarren, W. G. 1979. Some recent developments relating to statistical distributions in forestry and forest products research. In J. K. Ord, G. P. Patl, and C. Taillie, eds. Statistical distributions in ecological work. International Co-operative Publishing House, Fairland, MD. 1979.n

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Published

2007-06-27

Issue

Number 4 / Winter 1981

Section

Research Contributions

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