Comparison of estimation methods for fitting weibull distribution to the natural stand of Oluwa Forest Reserve, Ondo State, Nigeria

The relative performance of any distribution function truly depends on the estimation methods and where this is wrongly chosen poor fit is inevitable. This may mislead forest managers and thus thwart effort towards  sustainable forest management. This study therefore compared estimation methods for fitting 3-parameter  Weibull distribution to the natural stand of Oluwa Forest Reserve, Ondo State, Nigeria with a view to  enhancing sustainable management of the tree resources. Systematic sampling technique was used in the  laying of eight (8) temporary sample plots (TSPs) of size 50m x 50m in the natural forest. Three fitting  methods were used that based on maximum likelihood, moments and percentile. Comparison was based on  Kolmogorov-Smirnov statistic (K-S), bias, mean absolute error (MAE) and mean square error (MSE). The  result revealed that maximum likelihood method was more accurate in fitting the Weibull distribution to the  natural stand. It had the smallest mean bias and MSE values of 0.00009 and 0.00021, respectively. Maximum  likelihood method is therefore recommended for fitting the 3-parameter Weibull distribution to natural stand of  the reserve.Keywords: Weibull distribution, maximum likelihood, moments, percentile, natural stan

Comparison of Beta, Gamma Weibull Distributions for Characterising Tree Diameter in Oluwa Forest Reserve, Ondo State, Nigeria

This study compared the accuracy of the Beta, 2-parameter Gamma (2P) and 3-parameter Weibull (3P) distributions, fitted with the method of moments, for characterising the tree diameter of the reserve. Comparison was based on the Kolmogorov-Smirnov statistic (K-S), bias, mean absolute error (MAE), and mean square error (MSE). Distributions with location parameter were fixed as the minimum inventoried diameter of each plot.  A total of eight (8) temporary sample plots (TSPs) of size 50m x 50m were laid in the natural stand of the reserve. Systematic line transect was used in the laying of the plots. All trees with DBH ? 10.0cm in the selected plots were enumerated, identified and measured. The results from the goodness-of-fit statistics revealed that the Weibull (3P) distribution performed slightly better than the Beta distribution used in this study. The mean values for the K-S, bias, MAE, and MSE of the Weibull distribution were 0.11449, 0.00015, 0.00847, and 0.00022, respectively; as such ranked best. The Gamma (2P) distribution provided the worst fit to the dataset, with relatively large values for the goodness-of-fit statistics. It fits for the entire plot were far from the reverse J-shaped of natural forests, which implies that the Gamma (2P) distribution is inappropriate for determining the structure of the natural stand. Keywords: diameter characterisation, probability distribution, moments, natural fores

Evaluation of direct and indirect methods for modelling the joint distribution of tree diameter and height data with the bivariate Johnson’s SBB function to forest stands

Aim of study: In this study, both the direct and indirect methods by conditional maximum likelihood (CML) and moments for fitting Johnson’s SBB were evaluated. To date, Johnson’s SBB has been fitted by either indirect (two-stage) method using well-known procedures for the marginal diameter and heights, or direct methods, where all parameters are estimated at once. Application of bivariate Johnson’s SBB for predicting height and improving volume estimation requires a suitable fitting method.Area of study: E. globulus, P. pinaster and P. radiata stands in northwest Spain.Material and methods: The data set comprised of 308, 184 and 96 permanent sample plots (PSPs) from the aforementioned species. The suitability of the method was evaluated based on height and volume prediction. Indices including coefficient of determination (R2), root mean square Error (RMSE), model efficiency (MEF), Bayesian Information Criterion (BIC) and Hannan-Quinn Criterion (HQC) were used to assess the model predictions. Significant difference between observed and predicted tree height and volumes were tested using paired sample t-test at 5% level for each plot by species.Main results: The indirect method by CML was the most suitable method for height and volume prediction in the three species. The R2 and RMSE for height prediction ranged from 0.994 – 0.820 and 1.454 – 1.676, respectively. The percentage of plot in which the observed and predicted heights were significant was 0.32%. The direct method was the least performed method especially for height prediction in E. globulus.Research highlights: The indirect (two-stage) method, especially by conditional maximum likelihood, was the most suitable method for the bivariate Johnson’s SBB distribution.Keywords: conditional maximum likelihood; moments; two-stage method; direct method; tree volume

Modeling diameter distributions with six probability density functions in Pinus halepensis Mill. Plantations using low-density airborne laser scanning data in Aragón (northeast Spain)

Producción CientíficaThe diameter distributions of trees in 50 temporary sample plots (TSPs) established in Pinus halepensis Mill. stands were recovered from LiDAR metrics by using six probability density functions (PDFs): the Weibull (2P and 3P), Johnson’s SB, beta, generalized beta and gamma-2P functions. The parameters were recovered from the first and the second moments of the distributions (mean and variance, respectively) by using parameter recovery models (PRM). Linear models were used to predict both moments from LiDAR data. In recovering the functions, the location parameters of the distributions were predetermined as the minimum diameter inventoried, and scale parameters were established as the maximum diameters predicted from LiDAR metrics. The Kolmogorov–Smirnov (KS) statistic (Dn), number of acceptances by the KS test, the Cramér von Misses (W2) statistic, bias and mean square error (MSE) were used to evaluate the goodness of fits. The fits for the six recovered functions were compared with the fits to all measured data from 58 TSPs (LiDAR metrics could only be extracted from 50 of the plots). In the fitting phase, the location parameters were fixed at a suitable value determined according to the forestry literature (0.75·dmin). The linear models used to recover the two moments of the distributions and the maximum diameters determined from LiDAR data were accurate, with R2 values of 0.750, 0.724 and 0.873 for dg, dmed and dmax. Reasonable results were obtained with all six recovered functions. The goodness-of-fit statistics indicated that the beta function was the most accurate, followed by the generalized beta function. The Weibull-3P function provided the poorest fits and the Weibull-2P and Johnson’s SB also yielded poor fits to the data.Ministerio de Economía, Industria y Competitividad, Ayudas Torres Quevedo- (grant PTQ-16-08445)Fondo Europeo Agrario de Desarrollo Rural (FEADER) Programa de Desarrollo Rural de Aragón 2014-2020 - (project RF-64079

Modeling extreme values for height distributions in Pinus pinaster, Pinus radiata and Eucalyptus globulus stands in northwestern Spain

Methods of estimating extreme height values can be used in forest modeling to improve fits to the marginal distribution of heights in the following bivariate diameter-height models: the SBB Johnson’s distribution, the bivariate beta (GDB-2) distribution, the bivariate Logit-Logistic (LL-2) distribution and the power-normal (PN) distribution. Some applications to LiDAR derived data are also possible, e.g., for error calibration. Practical applications in forest management may also be considered, e.g., for pruning. In probability theory and statistics, the generalized extreme value (GEV) distribution, also known as the Fisher-Tippett distribution, is a family of continuous probability distributions that combine the Gumbel, Fréchet and Weibull distributions. This study compared the three distributions for fitting extreme values of tree heights (maximum and minimum heights), which were measured in 185 permanent research plots in Pinus pinaster Ait. stands, 97 research plots in Pinus radiata D. Don stands, and 128 research plots in Eucalyptus globulus Labill. Most of the eucalyptus stands were measured three times giving a total of 304 measurements. All plots are located in northwestern Spain. The Bias, Mean Absolute Error (MAE) and Mean Square Error (MSE) of the mean relative frequency of trees were used to evaluate the goodness-of-fit of the different functions, as well as the Kolmogorov-Smirnov statistic Dn. The Gumbel and the Weibull cumulative distribution functions (CDFs) proved suitable for describing extreme values of height distributions of the above-mentioned tree species in northwestern Spain. The Fréchet distribution was only used to model maximum values and yielded the poorest results in all casesGobierno del Principado de Asturias (Spain), project “Estudio del crecimiento y producción de Pinus pinaster Ait. en Asturias” (CN-07-094). Ministerio de Ciencia e Innovación (Spain), project “Influencia de los tratamientos selvícolas de claras en la producción, estabilidad mecánica y riesgo de incendios forestales en masas de Pinus radiata D. Don y Pinus pinaster Ait. en el Noroeste de España” (AGL2008-02259). Ministerio de Ciencia e Innovación (Spain) and ERDF programme (EU) for the period 2011-2013, project “Growth and yield modelling of clonal and seedling plantations of Eucalyptus globulus Labill. of NW Spain” (AGL2010-22308-C02-01). The Sustainable Forest Management Unit (UXFS) is funded by the Xunta de Galicia, Spain (“Consolidation and Structuring Program of Competitive Research Units 2011”) and by the ERDF programme (EU)S

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

The purpose of this study was to compare the accuracy of the Weibull, Johnson’s SB and beta distributions, fitted with some of the most usual methods and with different fixed values for the location parameters, for describing diameter distributions in even-aged stands of Pinus pinaster, Pinus radiata and Pinus sylvestris in northwest Spain. A total of 155 permanent plots in Pinus sylvestris stands throughout Galicia, 183 plots in Pinus pinaster stands throughout Galicia and Asturias and 325 plots in Pinus radiata stands in both regions were measured to describe the diameter distributions. Parameters of the Weibull function were estimated by Moments and Maximum Likelihood approaches, those of Johnson’s SB function by Conditional Maximum Likelihood and by Knoebel and Burkhart’s method, and those of the beta function with the method based on the moments of the distribution. The beta and the Johnson’s SB functions were slightly superior to Weibull function for Pinus pinaster stands; the Johnson’s SB and beta functions were more accurate in the best fits for Pinus radiata stands, and the best results of the Weibull and the Johnson’s SB functions were slightly superior to beta function for Pinus sylvestris stands. However, the three functions are suitable for this stands with an appropriate value of the location parameter and estimation of parameters methodEl objetivo de este estudio fue comparar la precisión de las distribuciones Weibull, SB de Johnson y beta, ajustadas por alguno de los métodos más habituales y fijando diferentes valores para los parámetros de localización, para describir distribuciones diamétricas en masas regulares de Pinus pinaster, Pinus radiata y Pinus sylvestris en el noroeste de España. Se midieron un total de 155 parcelas permanentes en masas de Pinus sylvestris en Galicia, 183 parcelas de Pinus pinaster en Galicia y en Asturias y 325 parcelas de Pinus radiata en ambas regiones para describir sus distribuciones diamétricas. Los parámetros de la función Weibull fueron estimados por las aproximaciones de los Momentos y Máxima Verosimilitud, los de la función SB de Johnson por los estimadores condicionados de Máxima Verosimilitud y por el método de Knoebel y Burkhart, y los de la función beta por el método basado en los Momentos de la distribución. Las funciones beta y SB de Johnson fueron ligeramente superiores a la función Weibull en las masas de Pinus pinaster; las funciones SB de Johnson y beta fueron más precisas en los mejores ajustes en las masas de Pinus radiata, y los mejores resultados de las funciones Weibull y SB de Johnson fueron ligeramente superiores a los de la función beta en las masas de Pinus sylvestris. No obstante, las tres funciones son apropiadas para estas masas siempre que se elija un valor de localización y método de estimación de los parámetros apropiadoThe present study was financially supported by the Gobierno del Principado de Asturias with the projects: “Estudio del crecimiento y producción en pinares regulares de Pinus radiata D. Don. en Asturias (PC04- 57)” and “Estudio del crecimiento y producción de Pinus pinaster Ait. en Asturias (CN-07-094)”; and by the Comisión Interministerial de Ciencia y Tecnología (CICYT) and the Comisión Europea with the projects: “Repoblación y gestión selvícola de Pino radiata y Pino de Oregón en Galicia (1FD97-0585-C03-03)” and “Crecimiento y evolución de masas de pinar en Galicia (AGL2001-3871-C02-01)”S

La ordenación de las poblaciones de fauna cinegética para la práctica de la caza. El caso del TECOR Oleiros-Rioaveso (Villalba, Lugo)

En este artículo se argumenta sobre la necesidad de los proyectos de ordenación de los recursos cinegéticos y se pone como ejemplo el caso del TECOR Oleiros-Rioaveso (Villalba, Lugo), en el que se hace una descripción del medio natural, del estado de las poblaciones de fauna con interés cinegético y se propone un plan de caza para las principales especies que pueblan o van a poblar el coto: corzo, jabalí, zorro, perdiz roja, faisán y aves migratorias. También se mencionan las principales actuaciones de mejora (en infraestructuras, sobre el medio y sobre las especies cinegéticas). Finalmente se expone el balance económico resultado de la ordenación

Application of extreme value distribution for assigning optimum fractions to distributions with boundary parameters: an eucalyptus plantations case study

The search for an optimum value to constrain boundary parameters in distribution models can be (and is) laborious and time-consuming. The accuracy of a distribution fit depends on the predetermined values of the boundary parameters. In this study, we applied the extreme value distributions derived from the generalized extreme value (GEV) in assigning the optimum constant to a distribution with boundary parameters. GEV subfamily (type 1), Gumbel’s distribution, was used to generate constant values which were used as a fraction of the minimum and maximum diameter and height data. The effectiveness of these values was established using five distribution models: logit-logistic (LL), Burr XII, Dagum, Kumaraswamy, and Johnson’s SB distributions. The distributions were fitted with maximum accuracy to the diameter and height data collected on 90 Eucalyptus camaldulensis Dehn sample plots. Model assessment was based on negative log-likelihood (-ΛΛ), Kolmogorov-Smirnov (K-S), Cramér-von Mises (W2), Reynold’s error index (EI), and mean square error (MSE). The result showed that the performance of the distributions was improved, especially for the height distribution, compared to other constant values. Gumbel’s distribution can be applied whenever (where) a boundary constraint is to be imposed on the location and scale parameters of the distribution models