An evaluation of ten estimators for fitting two-parameter weibull function to Nigerian forest stands

Year 2020, , 129 - 139, 15.06.2020

Friday Nwabueze Ogana

https://doi.org/10.31195/ejejfs.712992

Abstract

The quality fit produce by distribution function such as the Weibull depends to an extent the type of estimator used to derive its parameters. Inappropriate choice of estimator could affect management decision. Though several estimators have been developed for the Weibull function, there application to forestry have been relatively few. Therefore, this study evaluated ten estimators of the Weibull parameters using tree diameter data from five production forest plantations in Nigeria. The estimators were generalized least type I and type II, L-moment, moments, maximum likelihood, percentiles, rank correlation, least squares, U-statistics and weighted least squares. The quality of fits of the Weibull function were evaluated with several statistics including, Kolmogorov-Smirnov, Anderson-Darling, Cramer-von Mises, and so on. Relative rank sum from the evaluation statistics of the methods was analysed using One-way analysis of variance. The results showed that weighted least square had the smallest statistics and relative rank, but not significantly different from L-moment, moments and maximum likelihood (p > 0.05). The performances of least squares, generalized least type I and type II, percentiles and U-statistics were relatively poor. Thus, either the weighted least squares, moments-based or MLE could be used for the Weibull function in the forest stands in Nigeria.

Keywords

Moment-based methods, weighted least squares, maximum likelihood, Eucalyptus camaldulensis, Gmelina arborea

References

• Ajayi, S. (2013). Diameter Distribution for Gmelina arborea (roxb) plantation in Ukpon River Forest Reserve, Cross River state, Nigeria. AFREV STECH (An International Journal of Science and Technology). 2(1): 64-82, ISSN 2225-8612 (print); ISSN 2227-5444 (online)- (www.afrrevjo.net/stech; www.arronet.info.)
• Adedeji, O.H., Tope-Ajayi, O.O. and Abegunde, O.L. (2015). Assessing and predicting changes in the status of Gambari Forest Reserve, Nigeria using remote sensing and GIS techniques. Journal of Geographic Information System 7: 301-318
• Carretero, A.C. and Álvarez E.T. (2013). Modelling diameter distributions of Quercus suber L. stands in “Los Alcornocales” Natural Park (Cádiz-Málaga, Spain) by using the two parameter Weibull functions. Forest Systems 22(1): 15-24.
• Ekpa, N.E, Akindele, S.O. and Udofia, S.I. (2014). Gmelina arborea Roxb. Graded stands with the Weibull distribution Function in Oluwa Forest Reserve, Nigeria. International Journal of Agroforestry and Silviculture 1(9):110-113
• Gorgoso-Varela, J.J., Ogana, F.N. and Alonso Ponce, R. (2019). Evaluation of direct and indirect methods for modelling the joint distribution of tree diameter and height data with the bivariate Johnson’s SBB function of forest stands. Forest Systems 28(1) e004.
• Gorgoso-Varela, J.J. and Rojo-Alboreca, A. (2014). Short communication: 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.
• Gorgoso, J.J., Rojo, A., Camara-Obregon, A. and Dieguez-Aranda, U. (2012). A comparison of estimation methods for fitting Weibull, Johnson’s SB and beta functions to Pinus pinaster, Pinus radiata and Pinus sylvestris stands in northwest Spain. Forest Systems 21(3): 446-459.
• Gorgoso, J.J., Alvárez-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. Investigación Agrarian: Sistemas y Recursos Forestales 16(2): 113-123.
• Ige, P.O, Akinyemi, G.O. and Abi, E.A. (2013). Diameter Distribution Models for Tropical Natural Forest trees in Onigambari Forest Reserve. Journal of Natural Sciences Research, 3(12): 14 – 22.
• Ogana, F.N. and Ekpa, N.E. (2020). Modelling the non-spatial structure of Gmelina arborea Roxb stands in Oluwa Forest Reserve, Nigeria. Forestist (In press)
• Ogana, F.N., Chukwu, O. and Ajayi, S. (2020). Tree size distribution modelling: moving from complexity to finite mixture. Journal of Forest and Environmental Science 36(1): 7-16.
• Ogana, F.N. (2019). Bivariate modelling of diameter and height distributions of Eucalyptus plantations in Afaka forest reserves, Nigeria. [Postgraduate Thesis] University of Ibadan, Ibadan, Nigeria.
• Ogana, F.N., Osho, J.S.A. and Gorgoso-Varela, J.J. (2018). Application of extreme value distribution for assigning optimum fractions to distributions with boundary parameters: an eucalyptus plantations case study. Siberian Journal of Forest Sciences 4: 39-48.
• Ogana, F.N., Itam, E.S. and Osho, J.S.A. (2017). Modelling diameter distributions of Gmelina arborea plantation in Omo Forest Reserve, Nigeria with Johnson’s SB. Journal of Sustainable Forestry, 36(2): 123-133.
• Ogana, F.N. and Gorgoso-Varela, J.J. (2015). Comparison of estimation methods for fitting Weibull distribution to the natural stand of Oluwa Forest Reserve, Ondo State, Nigeria. Journal of Research in Forestry, Wildlife and Environment, 7(2): 81-90.
• Ogana, F.N., Osho, J.S.A. and Gorgoso-Varela, J.J. (2015). Comparison of beta, gamma and Weibull distributions for characterising tree diameter in Oluwa Forest Reserve, Ondo State, Nigeria. Journal of Natural Sciences Research 5(4): 28-36.
• Onyekwelu, J.C. (2001). Growth Characteristic and management scenarios for plantation grown Gmelina arborea and Nauclea diderichii in south-western Nigeria. Ph.D. thesis; Hieronymus Publishers, Munich; ISBN 3-89791-235-X
• Poudel, K.P. and Cao, Q.V. (2013). Evaluation of methods to predict Weibull parameters for characterising diameter distributions. Forest Science 59(2): 243-252.
• R Core Team. (2017). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL http://www.R-project.org/. (Visited on date: 30 /06/ 2017).
• Rubin, B.D., Manion, P.D. and Faber-langendoen, D. (2006). Diameter distributions and structural sustainability in forests. Forest Ecology and Management 222(1-3): 427-438.
• Sadani, S., Abdollahnezhad, K., Teimouri, M. and Ranjbar, V. (2019). A new estimator for Weibull distribution parameters: comprehensive comparative study for Weibull distribution. Statistics Computation arXiv:1902.05658.
• Saka, M.G. (2014). Growth and yield models for sustainable management of plantation-grown Eucalyptus species in Afaka Forest Reserve, Kaduna State, Nigeria. [Postgraduate Thesis] University of Ibadan, Ibadan, Nigeria.
• Sun, S., Cao, Q.V. and Cao, T. (2019). Characterizing diameter distributions for uneven-aged pine-oak mixed forests in the Qinling Mountains of China. Forests 10: 596, doi:10.3390/f10070596.
• Teimouri, M. (2020). ForestFit: Statistical modelling for plant size distributions. R package version 0.5.7. https://CRAN.R-project.org/package=ForestFit. Accessed 15 March 2020.
• Teimouri, M., Hoseini, S.M. and Nadarajah, S. (2013). Comparison of estimation methods for the Weibull distribution. Statistics, 47:93-109.
• Zhang, L., Kevin, C.P. and Chuanmin, L. (2003). A comparison of estimation methods for fitting Weibull and Johnson’s SB distributions to mixed spruce-fir stands in north-eastern North America. Canadian Journal of Forest Research. 33: 1340-1347.