Goodness-of-fit analysis on wood properties data from six Brazilian tropical hardwoods

Abstract

As part of a larger effort to develop design stresses for six hardwood species indigenous to tropical Brazil, a study was conducted to evaluate the relative goodness-of-fit of four distributions (normal, lognormal, Weibull, and SB) that are used in wood related applications to the characterization of the modulus of elasticity (MOE) and modulus of rupture (MOR) data obtained from tests on lumber and clear wood specimens. Three criteria [maximum likelihood, Kimball, and Kolmogorov-Smirnov (K-S)] were used to evaluate the distributions over their entire domain. The K-S test was also employed at the lower tail of the distributions to evaluate goodness-of-fit at this crucial location for design stress development. The results showed that with respect to both MOR and MOE, the SB distribution was as good or better than the other distributions. This was especially noticeable with the MOR data, since this data is often more skewed than MOE and the SB is particularly well suited to describe positively and negatively skewed data. The lognormal and the Weibull were both found to be useful under certain circumstances; the normal distribution, due to its lack of ability to characterize anything but symmetrical distributions, was found to be of virtually no value in this application. Significant distinctions were found between the structure of MOR and MOE data sets obtained from the tropical and temperate zone species. For reasons believed to be related to gross and anatomical structure, more skewness was found in the two temperate zone species studied than in the six tropical species. As such, the SB distribution, with its greater ability to quantify skewed data, performed overwhelmingly better than the other distributions. In describing the six tropical species, the advantage of the SB distribution was less pronounced.