Parameter Estimation of Weibull Growth Models in Forestry

International Journal of Mathematical Trends and Technology (IJMTT)          
© 2014 by IJMTT Journal
Volume-8 Number-3
Year of Publication : 2014
Authors : Dimpal Jyoti Mahanta , Munindra Borah


Dimpal Jyoti Mahanta , Munindra Borah. "Parameter Estimation of Weibull Growth Models in Forestry", International Journal of Mathematical Trends and Technology (IJMTT). V8:157-163 April 2014. ISSN:2231-5373. Published by Seventh Sense Research Group.

The main aim of this paper is to discuss some certain properties of three Weibull growth models in forestry viewpoint. The parameters of these models are estimated using Newton-Raphson iteration method for the mean diameter at breast height data and top height growth data originated from the Bowmont Norway spruce thinning experiment, sample plot 3661. The average height of 12 weeping Higan Cherry trees planted in Washington, D.C. is also used. The initial value specifications of the parameters for use of any iterative methods of estimation are also provided.


[1] J. J. Colbert, M. Schukers, D. Fekeduleng, J. Rentch, M.P. Mac Siurtain and K. Gottschalk, “Individual tree basal-area growth parameter estimates for four models,” Ecological Modelling, vol. 174, pp. 115-126, 2004.
[2] M. V. D. Colff and M. O. Kimberley, “A National height-age model for Pinus radiata in New Zealand,” New Zealand Journal of Forestry Science, vol. 43, no. 1, pp. 1-11, 2013.
[3] D. M. Dove, “Richness patterns in the parasite communities of exotic poeciliid fishes,” Parasitology, vol. 120, no. 6, pp. 609-623, 2000.
[4] N. R. Draper and H. Smith, Applied regression analysis, John Wiley & Sons Inc, New York, pp. 543–550, 1998.
[5] D. Fekedulegn, “Theoretical nonlinear mathematical models in forest growth and yield modelling,” Thesis, Department of Crop Science, Horticulture and Forestry, University College Dublin, Ireland, pp. 202, 1996.
[6] D. Fekedulegn, M.P. Mac Siurtain, and J.J. Colbert, “Parameter estimation of nonlinear growth models in forestry.” Silva Fennica, vol. 33, no. 4, pp. 327–336, 1999.
[7] U. P. Grosjean, “Growth model of the reared sea urchin Paracentrotus lividus (Lamarck, 1816),” Thesis submitted in fulfilment of the degree of Doctor, Agronomic Sciences and Biological Engineering, 2001.
[8] U. Karadavut, K. Kokten and Z. Kavurmaci, “Comparison of relative growth rates in silage corn cultivars,” Asian Journal of Animal and Veterinary Advances, vol. 5, no. 3, pp. 223-228, 2010.
[9] R. I. C. Lumbres, Y. J. Lee, F. G. Calora Jr and M. R. Parao, “Model fitting and validation of six height–DBH equations for Pinus kesiya Royle ex Gordon in Benguet Province, Philippines,” Forest Science and Technology, vol. 9, no. 1, pp. 45-50, 2013.
[10] H. B. Ozel and M. Ertekin, “Growth models in investigating oriental beech (Fagus orientalis Lipsky.) juvenilities growth performance in the Western Black Sea in Turkey (Devrek-Akçasu Case Study),” Romanian Biotechnological Letters, vol. 16, no. 1, pp. 5850-5857, 2011.
[11] D. A. Ratkowsky, Nonlinear Regression Modelling, Marcel Dekker, New York, 1983.
[12] G. A. F. Seber and C. J. Wild, Nonlinear Regression, A john Wiley & Sons Publication, ISBN 0-471-47135-6, 1989.
[13] L. Zhang, “Cross-validation of Non-linear Growth Functions for Modelling Tree Height Diameter Relationships,” Annals of Botany, vol. 79, pp. 251-257, 1997.
[14] Information on

Initial value, Parameter estimation, Weibull model, Newton-Raphson method, Growth model, derivative, Mathematical Properties.