Characterizing wood fiber and particle length with a mixture distribution and a segmented distribution
-
Quang V. Cao
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.
References
Anderson, T.W., Darling, D.A. (1954) A test of goodness of fit. J. Am. Stat. Assoc.49:765–769.10.1080/01621459.1954.10501232Search in Google Scholar
Borders, B.E., Patterson, W.D. (1990) Projecting stand tables –a comparison of the Weibull diameter distribution method, a percentile-based projection method, and a basal area growth projection method. For. Sci.36:413–424.Search in Google Scholar
Borders, B.E., Souter, R.A., Bailey, R.L. Ware, K.D. (1987) Percentile-based distributions characterize forest stand tables. For. Sci.33:570–576.Search in Google Scholar
Cao, Q.V. (2004) Predicting parameters of a Weibull function for modeling diameter distribution. For. Sci.50:682–685.Search in Google Scholar
Cao, Q.V., Burkhart, H.E. (1984) A segmented distribution approach for modeling diameter frequency data. For. Sci.30:129–137.Search in Google Scholar
Dodson, C.T.J. (1992) The effect of fiber length distribution on formation. J. Pulp Pap. Sci.18:J74–J76.Search in Google Scholar
Eckert, W.F., Masliyah, J.H., Afacan, A. (1997) Fractionation of softwood TMP by flotation. Tappi J.80:210–216.Search in Google Scholar
Gavin, D.G., Hu, F.S. (2005) Bioclimatic modeling using Gaussian mixture distributions and multiscale segmentation. Global Ecol. Biogeog.14:491–501.10.1111/j.1466-822x.2005.00171.xSearch in Google Scholar
Huber, P., Roux, J.C., Mauret, E., Belgacem, N., Pierre, C. (2003) Suspension crowding for a general fiber-length distribution: Application to flocculation of mixtures of short and long paper making fibers. J. Pulp Pap. Sci.29:77–85.Search in Google Scholar
Kropholler, H.W., Sampson, W.W. (2001) The effect of fiber length distribution on suspension crowding. J. Pulp Pap. Sci.27:301–305.Search in Google Scholar
Lee, B.J., McDonald, A.G., James, B. (2001) Influence of fiber length on the mechanical properties of wood-fiber/polypropylene prepreg sheets. Mater. Res. Innovat.4:97–103.10.1007/PL00010786Search in Google Scholar
Liu, C., Zhang, L., Davis, C.J., Solomon, D.S., Gove, J.H. (2002) A finite mixture model for characterizing the diameter distributions of mixed-species forest stands. For. Sci.48:653–661.Search in Google Scholar
Lu, J.Z., Monlezun, C.J., Wu, Q., Cao, Q.V. (2007) Fitting Weibull and lognormal distributions to wood fiber length. Wood Fiber Sci. In press.Search in Google Scholar
Mao, C.X., Colwell, R.K. (2005) Estimation of species richness: mixture models, the role of rare species, and inferential challenges. Ecology86:1143–1153.10.1890/04-1078Search in Google Scholar
Mark, R.E., Gillis, P.P. (1983) Structure and structural anisotropy. In: Handbook of Physical and Mechanical Testing of Paper and Paperboard. Eds. Mark, R.E., Murakami, K. Marcel Dekker, Inc., New York, NY. pp. 283–371.Search in Google Scholar
Mörling, T., Sjöstedt-de Luna, S., Svensson, I., Fries, A., Ericsson, T. (2003) A method to estimate fibre length distribution in conifers based on wood samples from increment cores. Holzforschung57:248–254.10.1515/HF.2003.038Search in Google Scholar
SAS Institute (2004) SAS/STAT 9.1 User's guide. SAS Institute, Inc., Cary, NC. 5121 pp.Search in Google Scholar
Svensson, I., Sjöstedt-de Luna, S., Bondesson, L. (2006) Estimation of wood fibre length distributions from censored data through an EM algorithm. Scandinavian J. Stat.33:503–522.10.1111/j.1467-9469.2006.00501.xSearch in Google Scholar
Takahashi, H., Suzuki, H., Endoh, K. (1979) The effect of fiber shape on the mechanical properties of paper and board. Tappi J.62:85–88.Search in Google Scholar
Tasman, J.E. (1972) The fiber length of Bauer-McNett screen fractions. Tappi J.55:136–138.Search in Google Scholar
Yan, J.F. (1975) A method for the interpretation of fiber length classification data. Tappi J.58:191–192.Search in Google Scholar
Zhang, L, Liu, C., Davis, C.J. (2004) A mixture model-based approach to the classification of ecological habitats using Forest Inventory and Analysis data. Can. J. For. Res.34:1150–1156.10.1139/x04-005Search in Google Scholar
©2007 by Walter de Gruyter Berlin New York
Articles in the same Issue
- Characterization of thin water layers in pulp by tritium exchange. Part 1: Methods development
- Characterization of thin water layers in pulp by tritium exchange. Part 2: Effect of refining on water absorption
- Characterizing wood fiber and particle length with a mixture distribution and a segmented distribution
- Effect of photolysis on 17th/18th century paper
- Changes in the cell wall volume of a number of wood species due to reaction with acetic anhydride
- A novel simple route to wood acetylation by transesterification with vinyl acetate
- Formation and properties of nanocomposites made up from solid aspen wood, melamine-urea-formaldehyde, and clay
- Ellagitannins from Portuguese oak wood (Quercus pyrenaica Willd.) used in cooperage: influence of geographical origin, coarseness of the grain and toasting level
- Epimeric phenylpropanoid glycosides from inner bark of Paulownia coreana Uyeki
- Lipid and lignin composition of woods from different eucalypt species
- A hysteresis model suitable for numerical simulation of moisture content in wood
- Simple estimation of critical stress intensity factors of wood by tests with double cantilever beam and three-point end-notched flexure
- Screening fungi tolerant to Western red cedar (Thuja plicata Donn) extractives. Part 1. Mild extraction by ultrasonication and quantification of extractives by reverse-phase HPLC
- Screening fungi tolerant to Western red cedar (Thuja plicata Donn) extractives. Part 2. Development of a feeder strip assay
- Contribution of hardness to the natural resistance of a range of wood species to attack by the marine borer Limnoria
- Biodeterioration of treated Pinus radiata timber by Australian decay fungi and the termite Coptotermes acinaciformis in laboratory bioassays and field conditions
- Development of an accelerated soil-contact decay test
- Obituary Dr. Bo Hortling (1942–2006)
Articles in the same Issue
- Characterization of thin water layers in pulp by tritium exchange. Part 1: Methods development
- Characterization of thin water layers in pulp by tritium exchange. Part 2: Effect of refining on water absorption
- Characterizing wood fiber and particle length with a mixture distribution and a segmented distribution
- Effect of photolysis on 17th/18th century paper
- Changes in the cell wall volume of a number of wood species due to reaction with acetic anhydride
- A novel simple route to wood acetylation by transesterification with vinyl acetate
- Formation and properties of nanocomposites made up from solid aspen wood, melamine-urea-formaldehyde, and clay
- Ellagitannins from Portuguese oak wood (Quercus pyrenaica Willd.) used in cooperage: influence of geographical origin, coarseness of the grain and toasting level
- Epimeric phenylpropanoid glycosides from inner bark of Paulownia coreana Uyeki
- Lipid and lignin composition of woods from different eucalypt species
- A hysteresis model suitable for numerical simulation of moisture content in wood
- Simple estimation of critical stress intensity factors of wood by tests with double cantilever beam and three-point end-notched flexure
- Screening fungi tolerant to Western red cedar (Thuja plicata Donn) extractives. Part 1. Mild extraction by ultrasonication and quantification of extractives by reverse-phase HPLC
- Screening fungi tolerant to Western red cedar (Thuja plicata Donn) extractives. Part 2. Development of a feeder strip assay
- Contribution of hardness to the natural resistance of a range of wood species to attack by the marine borer Limnoria
- Biodeterioration of treated Pinus radiata timber by Australian decay fungi and the termite Coptotermes acinaciformis in laboratory bioassays and field conditions
- Development of an accelerated soil-contact decay test
- Obituary Dr. Bo Hortling (1942–2006)