Abstract
The diameter distribution of 44 permanent plots (conifers and broadleaf trees) was modeled using the three-parameter Weibull and Johnson’s SB probability density functions (PDFs) in Santiago Papasquiaro, Durango. Four different methods of fitting parameters were used: maximum likelihood (ML), moments (MM), non-linear regression by ordinary least squares (ONLS) and percentiles (MP). The best method of fitting parameters for conifers and broadleaf trees was the method of moments. In modeling the Weibull PDFs, it was assumed that the location parameter (e) corresponds to the minimum measurable diameter. The scale parameter (λ) was modeled using the method of prediction parameter (PPM) through a linear regression relating to the quadratic mean diameter and dominant height of the stand. Finally, the shape parameter (γ) was indirectly recovered by the method of moments through prediction of the average diameter of the stand. According to the Kolmogorov-Smirnov test (P= 0.05), 71 % of the plots for the group of conifers and 68 % of the plots for the group of broadleaf species come from a population that follows the fitting distribution function.
References
Álvarez-González, J. G., & Ruiz-González, A. D. (1998). Análisis y modelización de las distribuciones diamétricas de Pinus pinaster Ait., en Galicia. Investigaciones Agrarias: Sistemas Recursos Forestales, 7(2), 123–137. http://www.inia.es/IASPF/1998/vol7/06.J.G.ALVAREZ.pdf
Bailey, R. L., & Dell, T. R. (1973). Quantifying diameter distributions with the Weibull function. Forest Science, 19, 97–104.
Borders, B. E. (1989). Systems of equations in forest stand modeling. Forest Science, 35, 548–556.
Borders, B. E., & Patterson, W. D. (1990). Projecting stand tables: A comparison of the Weibull diameter distribution method, a percentile-based projection method, and a basal area growth projection method. Forest Science, 36, 413–424.
Burk, T. E., & Newberry, J. D. (1984). A simple algorithm for moment-based recovery of Weibull distribution parameters. Forest Science, 30, 329–332.
Cao, Q. V., & Burkhart, H. E. (1984). A segmented distribution approach for modeling diameter frequency data. Forest Science, 30(1), 129–137.
Cao, Q. V. (2004). Predicting parameters of a Weibull function for modeling diameter distribution. Forest Science, 50, 682–685.
Cooray, K. (2006). Generalization of the Weibull distribution: The odd Weibull family. Statistical Modelling, 6, 265– 277. doi: https://doi.org/10.1191/1471082X06st116oa
Corral-Rivas, J. J., Vargas, L. B., Wehenkel, C., Aguirre, C. O., Álvarez, G. J. G., & Rojo, A. A. (2009). Guía para el establecimiento de sitios de investigación forestal y de suelos en bosques del estado de Durango. Durango, México: Editorial UJED.
Devore, J. L. (1987). Probability and statistics for engineers and the sciences. USA: Brooks/Cole Cengage learning.
Dubey, S. D. (1967). Some percentile estimators for Weibull parameters. Technometrics, 9, 119–129. doi: https://doi.org/10.1080/00401706.1967.10490445
García, M. E. (1981). Modificaciones al sistema de clasificación climática de Köppen (4ª ed.). México: Instituto de Geografía, Universidad Nacional Autónoma de México.
Gorgoso, J. J., Álvarez, G. J. G., Rojo, A., & Grandas-Arias, J. A. (2007). Modelling diameter distributions of Betula alba L. stands in northwest Spain with the two-parameter Weibull function. Investigaciones Agrarias: Sistemas Recursos Forestales, 16(2), 113–123. http://revistas.inia.es/index.php/fs/article/view/1002/999
Gorgoso-Varela, J. J., & Rojo-Alboreca, A. (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(3), 500–505. http://revistas.inia.es/index.php/fs/article/view/4939/2147
González-Elizondo, M. S., González, E. M., & Márquez, L. M. A. (2007). Vegetación y eco-regiones de Durango. México: CIIDIR-IPN-Plaza y Valdés, S. A. de C. V.
Hafley, W. L., & Schreuder, H. T. (1977). Statistical distributions for fitting diameter and height data in even-aged stands. Canadian Journal of Forest Research, 7, 481–487. doi: https://doi.org/10.1139/x77062
Hyink, D. M., & Moser, J. W. (1983). A generalized framework for projecting forest yield and stand structure using diameter distributions. Forest Science, 29, 85–95.
Jiang, L., & Brooks, J. (2009). Predicting diameter distributions for young longleaf pine plantations in Southwest Georgia. Southern Journal of Applied Forestry, 33, 25–28.
Johnson, N. L. (1949). Systems of frequency curves generated by methods of translation. Biometrika, 36, 149–176. doi: https://doi.org/10.1093/biomet/36.1-2.149
Knoebel, B. R., & Burkhart, H. E. (1991). A bivariate distribution approach to modeling forest diameter distribution at two points in time. Biometrics, 47, 241– 253. doi: https://doi.org/10.2307/2532509
Lai, C. D., Xie, M., & Murthy, D. N. P. (2003). A modified Weibull distribution. Reliability, IEEE Transactions, 52(1), 33–37. doi: https://doi.org/10.1109/TR.2002.805788
Leduc, D., Matney, T., Belli, K., & Baldwin, C., Jr. (2001). Predicting diameter distribution of longleaf pine plantations: A comparison between artificial neural networks and other accepted methodologies. Asheville, NC, USA: U. S. Department of Agriculture, Forest Service, Southern Research Station. http://www.srs.fs.usda.gov/pubs/rp/rp_srs025.pdf
Liu, C., Zhang, L., Davis, C. J., Solomon, D. S., & Gove, J. H. (2002). A finite mixture model for characterizing the diameter distributions of mixed–species forest stands. Forest Science 48(4), 653–661. http://www.fs.fed.us/ne/durham/4104/papers/Gove2002MixtureForestScience.pdf
Maldonado-Ayala, D., & Návar, J. J. (2002). Ajuste y predicción de la distribución Weibull a las estructuras diamétricas de plantaciones de pino de Durango, México. Madera y Bosques, 8(1), 61–72. http://www.redalyc.org/articulo.oa?id=61789905
Mehtätalo, L. (2004). An algorithm for ensuring compatibility between estimated percentiles of diameter distribution and measured stand variables. Forest Science 50, 20–32.
Návar, J. J., & Contreras, J. C. (2000). Ajuste de la distribución Weibull a las estructuras diamétricas de rodales irregulares de Pino de Durango, México. Agrociencia, 34, 353–361. http://www.redalyc.org/articulo.oa?id=30234312
Newby, M. (1980). The properties of moment estimators for the Weibull distribution based on the sample coefficient of variation. Technometrics, 22, 187–194. doi: https://doi.org/10.1080/00401706.1980.10486133
Parresol, B. (2003). Recovering of Johnson’s SB distribution. Asheville, NC, USA: U. S. Department of Agriculture, Forest Service, Southern Research Station. http://www.srs.fs.usda.gov/pubs/rp/rp_srs031.pdf
Rennolls, K., Geary, D. N., & Rollison, T. J. D. (1985). Characterizing diameter distributions by the use of the Weibull distribution. Forestry, 58(1), 57–66. doi: https://doi.org/10.1093/forestry/58.1.57
Statistical Analysis System (SAS Institute Inc.). (2008). SAS/ STATTM User´s Guide, Relase 8.0 Edition. Cary, NC, USA: Author.
Schreuder, H. T., Hafley, W. L., & Bennett, F. A. (1979). Yield prediction for unthinned natural slash pine stands. Forest Science, 25, 25–30.
Scolforo, J. R. S., Vitti, F. C., Grisi, R. L., Acerbi, F., & De Assis, A. L. (2003). SB distribution´s accuracy to represent the diameter distribution of Pinus taeda, through five fitting methods. Forest Ecology and Management, 175, 489–496. doi: https://doi.org/10.1016/S0378-1127(02)00183-4
Shifley, S., & Lentz, E. (1985). Quick estimation of the three-parameter Weibull to describe tree size distributions. Forest Ecology and Management, 13, 195– 203. doi: https://doi.org/10.1016/0378-1127(85)90034-9
Shiver, B. D. (1988). Sample sizes and estimation methods for the Weibull distribution for unthinned slash pine plantation diameter distributions. Forest Science, 34(3), 809–814.
Smalley, G. W., & Bailey, R. L. (1974). Yield tables and stand structure for loblolly pine plantations in Tennessee, Alabama and Georgia highlands. New Orleans, LA, USA: Forest Service, Southern Forest Experiment Station.
Sokal, R., & Rohlf, F. (1981). Biometry (2a ed.). New York, USA: W. H. Freeman and Company.
Secretaría de Recursos Naturales y Medio Ambiente (SRNyMA) (2006). Programa Estratégico Forestal 2030. Victoria de Durango, Dgo, México: Secretaría de Recursos Naturales y Medio Ambiente del Estado de Durango.
Torres-Rojo, J. M., Acosta-Mireles, M., & Magaña-Torres, O. S. (1992). Métodos para estimar los parámetros de la función Weibull y su potencial para ser predichos a través de atributos de rodal. Agrociencia. Serie Recursos Naturales, 2(2), 57–76.
Vanclay, J. (1995). Growth models for tropical forest: A synthesis of models and methods. Forest Science, 41, 7–42.
Wehenkel, C., Corral-Rivas, J. J., Hernández-Díaz, J. C., & Gadow, K. v. (2011). Estimating balanced structure areas in multi-species forests on the Sierra Madre Occidental, Mexico. Annals of Forest Science, 68, 385– 394. doi: https://doi.org/10.1007/s13595-011-0027-9
Wright, S. J., Muller-Landau, H. C., Condit, R., & Hubbell, S. P. (2003). Gap–dependent recruitment, realized vital rates, and size distributions of tropical trees. Ecology, 84(12), 3174–3185. doi: https://doi.org/10.1890/02-0038
Zanakis, S. H. (1979). A simulation study of some simple estimators for the three parameter Weibull distribution. Journal of Statistical Computation and Simulation, 9, 101–116. doi: https://doi.org/10.1080/00949657908810302
Zhang, L., Packard, K., & Liu, C. (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. doi: https://doi.org/10.1139/x03-054
Zhou, B., & McTague, J. P. (1996). Comparison and evaluation of five methods of estimation of the Johnson’s system parameters. Canadian Journal of Forest Research, 26(6), 928–935. doi: https://doi.org/10.1139/x26-102
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