Goodness-of-fit analysis for lumber data

Summary Four different probability distributions were studied to evaluate their relative goodness-of-fit in describing the modulus of rupture (MOR) and modulus of elasticity (MOE) of populations of dimension lumber. The distributions under consideration were the normal, lognormal, Weibull and Johnson's S_B. The populations of lumber consisted of 96 data sets of various species groups, mechanical properties, sizes, structural grades and growth regions. The goodness-of-fit criteria selected in this study were the log likelihood, Kimball and Kolmogorov-Smirnov (K-S) tests. The K-S statistic was also calculated at the value of the random variable associated with the lower five percent exclusion limit of the empirical cumulative distribution. This value indicated the degree of goodness-of-fit at the lower tail of the distribution. The results indicated that the S_B distribution generally provided the best fit to the data. The maximum likelihood test overwhelmingly recommended the S_B distribution. The Kimball and Kolmogorov-Smirnov tests gave milder endorsements of the S_B distribution. No distribution proved to be superior to the others in modeling the lower five percent exclusion limit of the populations.The author would like to thank the Engineering Data Management (EDM) Inc. of Fort Collins, Colorado, for the use of their parameter evaluation software, STAtistical Data MANager