Goodness-of-Fit for Mechanical Properties Distribution of Larch

Six different probability distributions, Johnson's SB, 2p-lognormal, 3p-lognormal, normal, 2p-Weibull, and 3p-Weibull, were used for testing their relative goodness of fit in describing modulus of rupture (MOR), modulus of elasticity (MOE), ultimate tension strength (UTS), and ultimate compression strength (UCS) of larch (Larix gmelini) dimension lumber. The populations of lumber consisted of 80 data sets with different mechanical properties, sizes, and structural grades. The Kolmogorov-Smirnov test was selected to be the goodness-of-fit criteria in this study. The 5- and 50-percentile values of these four different mechanical properties of larch lumber were estimated using both the inverse function of various distribution functions and the nonparametric method. Results indicated that 3p-lognormal was the optimal function in describing MOE of larch lumber. The 5- and 50-percentile estimations using the inverse function of 3p-lognormal were the closest values derived through the nonparametric method. Johnson's SB was the best one in describing MOR, UTS, and UCS. The 5- and 50-percentile estimations using the inverse function of Johnson's SB were the closest values derived with the nonparametric method. The distributions of these four mechanical properties of larch lumber were independent of the structural grade and size