Evaluation of four methods of fitting Johnson’s SBB for height and volume predictions

https://doi.org/10.17221/151/2017-JFSCitation:Ogana F.N. (2018): Evaluation of four methods of fitting Johnson’s SBB for height and volume predictions. J. For. Sci., 64: 187-197.
download PDF

Johnson’s SBB is the most commonly used bivariate distribution model in forestry. There are different methods of fitting Johnson’s distribution, and their accuracies differ. In this article, the method of conditional maximum likelihood (CML), moments, mode and Knoebel and Burkart (KB) were used to fit Johnson’s SBB distribution. A total of 4,237 diameter and height data obtained from 90 sample plots of Eucalyptus camaldulensis Dehnhardt were used. Evaluation was based on tree height and volume predictions. The predicted and observed tree heights and volumes were compared using the paired sample t-test. The average relative (%) bias and root mean square error of heights and volumes were computed for the four methods. The results showed that CML- and moments-based methods were more suitable than KB and mode methods for predicting tree height and volume. The level of significance and percentage bias were much lower in CML and moments. The mode-based method had the worst performance. The ranking order was: CML ≈ moments > KB > mode.

Fonseca T.F., Marques C.P., Parresol B.R. (2009): Describing maritime pine diameter distributions with Johnson’s SB distribution using a new all-parameter recovery approach. Forest Science, 55: 367–373.
Gorgoso J. J., Rojo A., Cámara-Obregón A., Diéguez-Aranda U. (2012): A comparison of estimation methods for fitting Weibull, Johnson’s SB and beta functions to Pinus pinaster, Pinus radiate and Pinus sylvestris stands in northwest Spain. Forest Systems, 21, 446-  https://doi.org/10.5424/fs/2012213-02736
Gorgoso-Varela Jose Javier, Rojo-Alboreca Alberto (2014): A comparison of estimation methods for fitting Weibull and Johnson’s SB functions to pedunculate oak (Quercus robur) and birch (Betula pubescens) stands in northwest Spain. Forest Systems, 23, 500-  https://doi.org/10.5424/fs/2014233-04939
Hafley W.L., Buford M.A. (1985): A bivariate model for growth and yield prediction. Forest Science, 31: 237–247.
Johnson N.L. (1949a): Systems of frequency curves generated by methods of translation. Biometrika, 36: 149–176.
Johnson N.L. (1949b): Bivariate distributions based on simple translation systems. Biometrika, 36: 297–304.
Knoebel Bruce R., Burkhart Harold E. (1991): A Bivariate Distribution Approach to Modeling Forest Diameter Distributions at Two Points in Time. Biometrics, 47, 241-  https://doi.org/10.2307/2532509
Li F., Zhang L., Davis C.J. (2002): Modeling the joint distribution of tree diameters and heights by bivariate generalized beta distribution. Forest Science, 48: 47–58.
Mønness Erik (2015): The bivariate power-normal distribution and the bivariate Johnson system bounded distribution in forestry, including height curves. Canadian Journal of Forest Research, 45, 307-313  https://doi.org/10.1139/cjfr-2014-0333
Nanang D.M. (2002): Statistical distributions for modelling stand structure of neem (Azadirachta indica) plantations. Journal of Tropical Forest Science, 14: 456–473.
Ogana Friday N., Itam Ekaette S., Osho Johnson S. A. (2016): Modeling diameter distributions of Gmelina arborea plantation in Omo Forest Reserve, Nigeria with Johnson’s S B. Journal of Sustainable Forestry, 36, 121-133  https://doi.org/10.1080/10549811.2016.1263575
Ogana F.N., Osho J.S.A., Gorgoso-Varela J.J. (2018): An approach to modeling the joint distribution of tree diameter and height data. Journal of Sustainable Forestry, , 1-14  https://doi.org/10.1080/10549811.2017.1422434
Omule S.A.Y. (1984): Fitting Height-diameter Curves. Research Report RR84008-HQ. Victoria, British Columbia Ministry of Forests: 19.
Petráš R., Mecko J., Nociar V. (2010): Diameter structure of the stands of poplar clones. Journal of Forest Science, 56, 165-170  https://doi.org/10.17221/65/2009-JFS
Rupšys P., Petrauskas E. (2010): The bivariate Gompertz diffusion model for tree diameter and height distribution. Forest Science, 56: 271–280.
Schreuder H. T., Hafley W. L. (1977): A Useful Bivariate Distribution for Describing Stand Structure of Tree Heights and Diameters. Biometrics, 33, 471-  https://doi.org/10.2307/2529361
Tewari V.P, Gadow K.V (1999): Modelling the relationship between tree diameters and heights using SBB distribution. Forest Ecology and Management, 119, 171-176  https://doi.org/10.1016/S0378-1127(98)00520-9
Wang M., Rennolls K. (2007): Bivariate distribution modeling with tree diameter and height data. Forest Science, 53: 16–24.
Zhang Lianjun, Packard Kevin C, Liu Chuangmin (2003): A comparison of estimation methods for fitting Weibull and Johnson's SB distributions to mixed spruce–fir stands in northeastern North America. Canadian Journal of Forest Research, 33, 1340-1347  https://doi.org/10.1139/x03-054
Zhou Bailin, McTague John Paul (1996): Comparison and evaluation of five methods of estimation of the Johnson system parameters. Canadian Journal of Forest Research, 26, 928-935  https://doi.org/10.1139/x26-102
download PDF

© 2022 Czech Academy of Agricultural Sciences | Prohlášení o přístupnosti