An approach to modeling the joint distribution of tree diameter and height data

References

• Burkhart, H. E., & Tomé, M. (2012). Modeling forest trees and stands (2nd ed., p. 457). New York, USA: Springer Science & Business Media Dordrecht. doi:10.1007/978-90-481-3170-9
   Google Scholar
• Burr, I. W. (1942). Cumulative frequency functions. Annals of Mathematical Statistics, 13, 215–232.
   Google Scholar
• Gorgoso-Varela, J. J., García-Villabrille, J. D., & Rojo-Alboreca, A. (2015). Modeling extreme values for height distributions in Pinus pinaster, Pinus radiata and Eucalyptus globulus stands in northwestern Spain. iForest, 9, 23–29.
   Web of Science ®Google Scholar
• Gorgoso-Varela, J. J., Garcia-Villabrille, J. D., Rojo-Alboreca, A., Gadow, K., & Alvarez-Gonzalez, J. G. (2016). Comparing Joshnson’s SBB, Weibull and Logit-Logistic bivariate distributions for modelling tree diameters and heights using copulas. Forest Systems, 25(1), 1–5.
   Web of Science ®Google Scholar
• Gorgoso-Varela, J. J., & Rojo-Alboreca, A. (2014). Use of Gumbel and Weibull functions to model extreme values of diameter distributions in forest stands. Annals of Forest Science, 71(7), 741–750.
   Web of Science ®Google Scholar
• Hafley, W. L., & Buford, M. A. (1985). A bivariate model for growth and yield prediction. Forest Sciences, 31, 237–247.
   Web of Science ®Google Scholar
• Hafley, W. L., & Schreuder, H. T. (1977). A useful bivariate distribution for describing stand structure of tree heights and diameters. Biometrics, 33, 471–478.
   Web of Science ®Google Scholar
• Johnson, N. L. (1949). Systems of frequency curves generated by methods of translation. Biometrika, 36, 149–176.
   PubMed Web of Science ®Google Scholar
• Knoebel, B. R., & Burkhart, H. E. (1991). A bivariate distribution approach to modeling forest diameter distributions at two points in time. Biometrics, 47, 241–253.
   Web of Science ®Google Scholar
• Kumaraswamy, P. (1980). A generalized probability density functions for double-bounded random processes. Journal of Hydrology, 46(1–2), 79–88.
   Web of Science ®Google Scholar
• Li, F., Zhang, L., & Davis, C. J. (2002). Modeling the joint distribution of tree diameters and heights by bivariate generalized beta distribution. Forest Sciences, 48(1), 47–58.
   Web of Science ®Google Scholar
• Lindsay, S. R., Wood, G. R., & Woollons, R. C. (1996). Modelling the diameter distribution of forest stands using Burr distribution. Journal of Applied Statistics, 23(6), 609–619.
   Web of Science ®Google Scholar
• Mardia, K. V. (1970). Families of bivariate distributions (p. 231). London, UK: Griffin.
   Google Scholar
• Mønness, E. (2015). The bivariate power-normal and the bivariate Johnson’s system bounded distribution in forestry, including height curves. Canadian Journal of Forest Research, 45, 307–313.
   Google Scholar
• Nanang, D. M. (2002). Statistical distributions for modelling stand structure of neem (Azadirachta indica) plantations. Journal of Tropical Forest Science, 14(4), 456–473.
   Google Scholar
• Petras, R., Mecko, J., & Nociar, V. (2010). Diameter structure of the stands of poplar clones. Journal of Forest Science, 56(4), 165–170.
   Google Scholar
• Plackett, R. L. (1965). A class of bivariate distributions. Journal American Statistical Association, 60, 516–522.
   Web of Science ®Google Scholar
• Podlaski, R. (2016). Highly skewed and heavy-tailed tree diameter distributions: Approximation using the gamma shape mixture model. Canadian Journal of Forest Research, 46(11), 1275–1283.
   Google Scholar
• Podlaski, R. (2017). Forest modeling: The gamma shape mixture model and simulation of tree diameter distributions. Annals of Forest Science, 74(2), 29.
   Web of Science ®Google Scholar
• R Core Team. (2016). R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing. Retrieved from http://www.R-project.org/
   Google Scholar
• Rupsys, P., & Petrauskas, E. (2010). The bivariate Gompertz diffusion model for tree diameter and height distribution. Forest Sciences, 56(3), 271–280.
   Web of Science ®Google Scholar
• Tewari, V. P., & Von Gadow, K. (1997). Fitting a bivariate distribution to diameter-height data of forest trees. Indian Forester, 123, 815–820.
   Google Scholar
• Tewari, V. P., & Von Gadow, K. (1999). Modeling the relationship between tree diameters and heights using SBB distribution. Forest Ecology and Management, 119, 171–176.
   Web of Science ®Google Scholar
• Wang, M. (2005). Distributional Modeling in forestry and remote sensing. PhD thesis, Univ. of Greenwich, London, UK, 187
   Google Scholar
• Wang, M., & Rennolls, K. (2005). Tree diameter distribution modeling: Introducing the Logit-Logistic distribution. Canadian Journal of Forest Research, 35, 1305–1313.
   Web of Science ®Google Scholar
• Wang, M., & Rennolls, K. (2007). Bivariate distribution modeling with tree diameter and height data. Forest Sciences, 53(1), 16–24.
   Web of Science ®Google Scholar
• Wang, M., Rennolls, K., & Tang, S. (2008). Bivariate distribution modelling with tree diameter and height: Dependency modelling using copulas. Forest Sciences, 54(3), 284–293.
   Web of Science ®Google Scholar
• Zucchini, W., Schmidt, M., & Von Gadow, K. (2001). A model for the diameter-height distribution in an uneven-aged beech forest and a method to assess the fit of such models. Silva Fenn, 35(2), 169–183.
   Web of Science ®Google Scholar