Characterizing wood fiber and particle length with a mixture distribution and a segmented distribution

Abstract The length data from 12 samples of wood fibers and particles were described using lognormal and Weibull distributions. While both distributions fitted the middle range of the data well, the lognormal distribution provided a closer fit for short fibers and particles and the Weibull distribution was more appropriate for long ones. A mixture of the lognormal and Weibull distributions was developed using a variable weight to allow the new distribution to take the lognormal form for short fibers and gradually change to the Weibull form for long fibers. In the segmented distribution approach, a left segment of the lognormal distribution was joined to a right segment from the Weibull form. The Anderson-Darling goodness-of-fit test at the 5% level failed to reject the hypothesis that the mixture distribution and the segmented distribution fitted the data. Q-Q plots showed that both the mixture and segmented distributions provided an excellent fit to the fiber and particle length data, combining the best features of the lognormal and the Weibull distributions. These two new distributions are therefore better alternatives than the single lognormal and Weibull distributions for this data set.