Trivariate distribution modeling of tree diameter, height, and volume

Forest Science

Volumn 56, Issue 3, 2010, Pages 290-300

  Wang, Mingliang ^a   Upadhyay, Anoop ^b   Zhang, Lianjun ^c  

^a LAURENTIAN FORESTRY CENTRE   (Canada)

^b Project Policy and Planning ^*  (India)

^c STATE UNIVERSITY OF NEW YORK   (United States)

Author keywords

Johnson's sBBB; Normal copula

Indexed keywords

DISTRIBUTION MODELS; EMPIRICAL DISTRIBUTION FUNCTIONS; LOG-LOGISTIC; LOGISTIC DISTRIBUTIONS; MARGINAL DISTRIBUTION; MATHEMATICAL FUNCTIONS; MODEL PARAMETERS; MULTIVARIATE DISTRIBUTIONS; REGRESSION MODEL; SEMIPARAMETRIC; TREE DIAMETER; TRIVARIATE; TWO STAGE; UNIVARIATE DISTRIBUTIONS; VOLUME DISTRIBUTIONS; WEIBULL;

REGRESSION ANALYSIS; TREES (MATHEMATICS); WEIBULL DISTRIBUTION;

DISTRIBUTION FUNCTIONS;

EID: 77953907811     PISSN: 0015749X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (33)

1. Andersen, H., S.E. Reutebuch, and R.J. McGaughey. 2006. A rigorous assessment of tree height measurements obtained using airborne LIDAR and conventional field methods. Can. J. Remote Sens. 32(5):355-366.
2. Anderson, T.W. 1984. An introduction to multivariate statistical analysis, 2nd ed. Wiley, New York, NY. 675 p.
3. Bailey, R.L., and T.R. Dell. 1973. Quantifying diameter distri-butions with the Weibull function. For. Sci. 19:97-104.
4. Clemen, R.T., and T. Reilly. 1999. Correlations and copulas for decision and risk analysis. Manag. Sci. 45:208-224.
5. Genest, C., and J. Mackay. 1986. The joy of copulas: Bivariate distributions with uniform marginals. Am. Statist. 40:280-283.
6. Hafley, W.L., and M.A. Buford. 1985. A bivariate model for growth and yield prediction. For. Sci. 31:237-247.
7. Joe, H. 1997. Multivariate models and dependence concepts. Chapman and Hall, London, UK. 399 p.
8. Johnson, N.L. 1949a. Systems of frequency curves generated by methods of translation. Biometrika 36:149-176.
9. Johnson, N.L. 1949b. Bivariate distributions based on simple translation systems. Biometrika 36:297-304.
10. Knoebel, B.R., and H.E. Burkhart. 1991. A bivariate distribution approach to modelling forest diameter distributions at two points of time. Biometrics 47:241-253.
11. Lee, L.F. 1983. Generalized econometric models with selectivity. Econometrica 51:507-512.
12. Li, F., L. Zhang, and C.J. Davis. 2002. Modeling the joint distribution of tree diameters and heights by bivariate generalized distribution. For. Sci. 48(1):47-58.
13. Maltamo, M., K. Mustonen, J. Hyyppa, J. Pitkanen, and X. Yu. 2004. The accuracy of estimating individual tree variables with airborne laser scanning in a boreal nature. Can. J. For. Res. 34:1791-1801.
14. Mardia, K.V. 1970. Families of bivariate distributions. Griffin, London, UK. 109 p.
15. Mathsoft. 1999. S-Plus 2000 guide to statistics, Vol. 1. Data Analysis Products Division, Mathsoft, Inc., Seattle, WA.
16. Nelsen, R.B. 1999. An introduction to copulas. Springer, New York, NY. 216 p.
17. Plackett, R.L. 1965. A class of bivariate distributions. J. Am. Stat. Assoc. 60:516-522.
18. Rennolls, K., D.N. Geary, and T.J.D. Rollinson. 1985. Characterizing diameter distributions by the use of the Weibull distribution. Forestry 58(1):57-66.
19. Rennolls, K., and M. Wang. 2005. A new parameterization of Johnson's SB distribution with application to fitting forest tree diameter data. Can. J. For. Res. 35(3):575-579.
20. Schreuder, H.T., and W.L. Hafley. 1977. A useful bivariate distribution for describing stand structure of tree heights and diameters. Biometrics 33:471-478.
21. Schreuder, H.T., H.T. Bhattacharya, and J.P. McClure. 1982a. Towards a unified distribution theory for stand variables using SBBB distribution. Biometrics 38:137-142.
22. Schreuder, H.T., H.T. Bhattacharya, and J.P. McClure. 1982b. The SBBB distribution: A potentially useful trivariate distribution. Can. J. For. Res. 12:641-645.
23. Schumacher, F.X., and F. Hall. 1933. Logarithmic expression of timber-tree volume. J. Agric. Res. 47:719-734.
24. Sklar, A. 1959. Fonctions de répartition à n dimensions et leurs marges. Publ. Inst. Statist. Univ. Paris 8:229-231.
25. Sklar, A. 1973. Random variables, joint distribution functions and copulas. Kybernetika 9:449-460.
26. Spurr, S.H. 1952. Forest inventory. Ronald Press Co., New York, NY. 476 p.
27. Tadikamalla, P.R., and N.L. Johnson. 1982. Systems of fre-quency curves generated by transformations of logistic variables. Biometrika 69(2):461-465.
28. Tewari, V.P., and K.V. Gadow. 1999. Modelling the relationship between tree diameters and heights using SBB distribution. For. Ecol. Manag. 119:171-176.
29. Wang, M., and K. Rennolls. 2005. Tree diameter distribution modelling: Introducing the logit-logistic. Can. J. For. Res. 35(6):1305-1313.
30. Wang, M., and K. Rennolls. 2007. Bivariate distribution mod-elling with tree diameter and height data. For. Sci. 53(1):16-24.
31. Wang, M., K. Rennolls, and S. Tang. 2008. Bivariate distribu-tion modeling of tree diameters and heights: Dependency modeling using copulas. For. Sci. 54(3):284-293.
32. Weibull, W. 1951. A statistical distribution function of wide applicability. J. Appl. Mech. 18(3):293-297.
33. Zucchini, W., M. Schmidt, and K.V. Gadow. 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.