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Evaluation of estimation methods for parameters of the probability functions in tree diameter distribution modeling | ||
| Environmental Resources Research | ||
| دوره 8، شماره 1، فروردین 2020، صفحه 25-40 اصل مقاله (951.2 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22069/ijerr.2020.5086 | ||
| نویسندگان | ||
| M. Teimouri* 1؛ K. Abdolahnezhad2؛ Sh. Ghalandarayeshi1 | ||
| 1Assistant Professor, Gonbad Kavous University, Gonbad Kavous, Iran | ||
| 2Assistant Professor, Golestan University, Gorgan, Iran | ||
| چکیده | ||
| One of the most commonly used statistical models for characterizing the variations of tree diameter at breast height is Weibull distribution. The usual approach for estimating parameters of a statistical model is the maximum likelihood estimation (likelihood method). Usually, this works based on iterative algorithms such as Newton-Raphson. However, the efficiency of the likelihood method is not guaranteed since there is no assurance that the Newton-Raphson method for maximizing the log-likelihood function will converge. In such cases, one option is to use a better estimation approach. In this study, several methods were compared for estimating the parameters of two- and three-parameter Weibull distributions. We applied ten methods for two-parameter and twelve methods for three-parameter cases. The data set was collected from natural beech dominated forest in northern Iran. The results demonstrated that among the estimators investigated for two-parameter Weibull distribution, the percentile method outperformed other competitors. In contrast, for three-parameter Weibull distribution, the trimmed L-moment (TL-moment) method and the modified method of moments (type I and type II) outperformed other competitors in terms of Cramer Von-Mises criterion and Kolmogorov-Smirnov criterion, respectively. | ||
| کلیدواژهها | ||
| Least square method؛ Method of maximum product spacings؛ TL-moment؛ Weibull distribution؛ Weighted maximum likelihood estimator | ||
| مراجع | ||
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Abdul-Moniem, I.B. 2007. L-moments and TL-moments estimation for the exponential distribution. Far East Journal of Theoretical Statistics, 23, 1. 51.
Bailey, R.L., and Dell, T.R. 1973. Quantifying diameter distributions with the Weibull function. Forest Science, 19 (2), 97-104. Burkhart, H.E., and Tomé, M. 2012. Modeling forest trees and stands. Springer Science & Business Media. Cheng, R.C.H., and Amin, N.A.K. 1979. Maximum product of spacings estimation with application to the lognormal distribution. Math Report, 791p. Cheng, R.C.H., and Amin, N.A.K. 1983. Estimating parameters in continuous univariate distributions with a shifted origin. Journal of the Royal Statistical Society. Series B (Methodological), pp. 394-403.
Cohen, C.A., and Whitten, B. 1982. Modified maximum likelihood and modified moment estimators for the three-parameter Weibull distribution. Communications in Statistics-Theory and Methods, 11 (23), 2631-2656.
Coomes, D.A., and Allen, R.B. 2007. Mortality and tree-size distributions in natural mixed-age forests. Journal of Ecology, 95 (1), 27-40. Cousineau, D. 2009. Nearly unbiased estimators for the three-parameter Weibull distribution with greater efficiency than the iterative likelihood method. British Journal of Mathematical and Statistical Psychology, 62, 167-191.
Dodson, B. 2006. The Weibull Analysis Handbook. ASQ Quality Press. Duan, A.G., Zhang, J.G., Zhang, X.Q., and He, C.Y. 2013. Stand diameter distribution modelling and prediction based on Richards function. PloS one, 8(4), e62605.
Elamir, E.A.H., and Seheult, A.H. 2003. Trimmed L-moments. Computational Statistics & Data Analysis, 43 (3), 299-314. Engeman, R.M., and Keefe, T.J. 1982. On generalized least squares estimation of the Weibull distribution. Communications in Statistics-Theory and Methods, 11 (19), 2181-2193.
Ghalandarayeshi, S., 2019. Modeling diameter distribution of Fagus orientals Lipsky using probability density functions (Case study in Kordkoy-Golestan province). In, The 2nd National Conference on Natural Resources Management. Gonbad Kavous Univerity, pp. 1-6.
Ghalandarayeshi, Sh., Nord-Larsen, T., Kvist Johannsen, V., and Bo Larsen, J. 2017. Spatial patterns of tree species in Suserup Skov-a semi-natural forest in Denmark. Forest Ecology and Management, 406, 391-401. M. Teimouri et al. / Environmental Resources Research 8, 1 (2020) 39 G.N.R.W.M. 2017. Forest management plan. Technical report, Golestan Natural Resources and Watershed Management.
Gorgoso, J.J., Álvarez González, J.G., Rojo, A., and Grandas-Arias, J.A. 2007. Modelling diameter distributions of Betula alba L. stands in northwest Spain with the two-parameter Weibull function. Forest Systems, 16 (2), 113-123.
Hassanein, Kh.M. 1971. Percentile estimators for the parameters of the Weibull distribution. Biometrika, 58 (3), 673-676. Hosking, J.R.M. 1990. L-moments: analysis and estimation of distributions using linear combinations of order statistics. Journal of the Royal Statistical Society. Series B (Methodological), pp. 105-124.
Hung, W.L. 2001. Weighted least-squares estimation of the shape parameter of the Weibull distribution. Quality and Reliability Engineering International, 17 (6), 467-469.
Hyink, D.M., and Moser, J.W. 1983. A generalized framework for projecting forest yield and stand structure using diameter distributions. Forest Science, 29 (1), 85-95.
Jacquelin, J. 1993. Generalization of the method of maximum likelihood. IEEE Transactions on Electrical Insulation, 28 (1), 65-72.
Kantar, Y.M. 2015. Generalized least squares and weighted least squares estimation methods for distributional parameters. REVSTAT-Statistical Journal, 13 (3), 263-282.
Kilkki, P., Maltamo, M., Mykkänen, R., and Päivinen, R. 1989. Use of the Weibull function in estimating the basal area dbh-distribution. Silva Fennica, 23 (4), 311-318.
Kurdi, M., Soltani-Mohammadi, S., Eslamkish, T., and Larina, N. 2017. Evaluating the performance of concentration-number (cn) fractal model for separation of soil horizon regarding vertical distribution and 3d models. Journal of Tethys, 5 (4), 337-349.
Lei, Y. 2008. Evaluation of three methods for estimating the Weibull distribution parameters of Chinese pine (Pinus tabulaeformis). Journal of Forest Science, 54 (12), 566-571.
Little, S.N. 1983. Weibull diameter distributions for mixed stands of western conifers. Canadian Journal of Forest Research, 13 (1), 85-88. Merganič, J., and Sterba, H. 2006. Characterisation of diameter distribution using the Weibull function: method of moments. European Journal of Forest Research, 125 (4), 427-439.
Newton, P.F., Lei, Y., and Zhang, S.Y. 2005. Stand-level diameter distribution yield model for black spruce plantations. Forest Ecology and Management, 209 (3), 181-192.
Norman, L.J., Kotz, S., and Balakrishnan, N. 1994. Continuous Univariate Distributions, volume I. John Wiley & Sons. Prabhakar Murthy, D.N., Xie, M., and Jiang, R. 2004. Weibull Models, volume 505. John Wiley & Sons. R Core Team. 2018. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. Available from URL:https://www.R-project.org/. Reynolds, M.R., Burk, T.E., and Huang. W.Ch. 1988. Goodness-of-fit tests and model selection procedures for diameter distribution models. Forest Science, 34 (2), 373-399.
Stankova, T.V., and Zlatanov, T.M. 2010. Modeling diameter distribution of Austrian black pine (Pinus nigra Arn.) plantations: a comparison of the Weibull frequency distribution function and percentile-based projection methods. European Journal of Forest Research, 129 (6), 1169-1179.
Teimouri, M., and Nadarajah, S. 2012. A simple estimator for Weibull shape parameter. International Journal of Structural Stability and Dynamics, 12 (2), 395-402. Teimouri, M., Hoseini, S.M., and Nadarajah, S. 2013. Comparison of estimation methods for the Weibull distribution. Statistics, 47 (1), 93-109.
Teimouri, M., Doser, J.W., and Finley, A.O. 2020. ForestFit: An R package for modeling plant size distributions, Environmental Modelling & Software, 131: 104668, doi:10.1016/j.envsoft.2020.104668. Tiryakioğlu, M., and Hudak, D. 2007. On estimating Weibull modulus by the linear regression method. Journal of Materials Science, 42 (24), 10173-10179.
Van Zyl, J.M., and Schall, R. 2012. Parameter estimation through weighted least-squares rank 40 M. Teimouri et al. / Environmental Resources Research 8, 1 (2020) regression with specific reference to the Weibull and Gumbel distributions. Communications in Statistics-Simulation and Computation, 41 (9), 1654-1666.
Wang, F.K., and Keats, J.B. 1995. Improved percentile estimation for the two-parameter Weibull distribution. Microelectronics Reliability, 35 (6), 883-892.
Wayne, N. 1982. Applied Life Data Analysis. John Wiley & Sons, New York. Zhang, L., Packard, K.C., and Liu, Ch. 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 (7), 1340-1347.
Zhang, L., and Liu, Ch. 2006. Fitting irregular diameter distributions of forest stands by Weibull, modified Weibull, and mixture Weibull models. Journal of Forest Research, 11 (5), 369-372.
Zhang, L.F., Xie, M., and Tang, L.C. 2008. On weighted least squares estimation for the parameters of Weibull distribution. In Recent Advances in Reliability and Quality in Design, Pp: 57-84. Springer.
Zhang, X., Lei, Y., and Cao, Q.V. 2010. Compatibility of stand basal area predictions based on forecast combination. Forest Science, 56 (6), 552-557. | ||
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