Comparación de métodos de estimación de ajuste de las funciones Weibull, SB de Johnson y beta a masas de Pinus pinaster, Pinus radiata y Pinus sylvestris en el noroeste de España

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 Burhart’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 method.El 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 apropiado

Modelización de las distribuciones diamétricas en masas de Betula alba L. en el noroeste de España con la función Weibull biparamétrica

The diameter distributions of 125 permanent plots installed in birch dominated (Betula alba L.) stands in Galicia were modelled with the two-parameter Weibull distribution. Four different fitting methods were used: that based on percentiles of the distribution, non linear regression, maximum likelihood and the method of moments. The most accurate fit was obtained with the non linear regression (NLR) approach, considering the following statistics in the comparison: bias, mean absolute error (MAE), mean square error (MSE) and number of plots rejected by the Kolmogoroff-Smirnoff (KS) test. The scale parameter (b) and the shape parameter (c) obtained with the most accurate method (non linear regression), were first modelled with simple linear models and then related to commonly measured prediction variables (quadratic mean diameter, dominant height and stand density) with the parameter prediction model (PPM). The parameters fitted with the method of moments were recovered with the parameter recovery model (PRM) from the first and the second moments of the distribution (mean diameter and variance, respectively). Results indicated that both methods were successful in predicting the diameter frequency distributions. The PRM was more accurate than the PPM method.Las distribuciones diamétricas de 125 parcelas permanentes instaladas en masas puras de abedul (Betula alba L.) en Galicia fueron modelizadas con la distribución Weibull de dos parámetros. Se emplearon cuatro métodos de ajuste: basados en percentiles de la distribución, regresión no lineal, máxima verosimilitud y el método de los momentos. Los ajustes más precisos fueron obtenidos con regresión no lineal, considerando los siguientes estadísticos en la comparación de los resultados: sesgo, error medio absoluto, error medio cuadrático y número de parcelas rechazadas por el test de Kolmogoroff-Smirnoff. El parámetro de escala (b) y el parámetro de forma (c) obtenidos con el método más preciso (regresión no lineal), fueron relacionados con variables de masa de frecuente medición (diámetro medio cuadrático, altura dominante y densidad) mediante modelos lineales sencillos aplicando la metodología de predicción de parámetros. Los parámetros ajustados con el método de los momentos fueron recuperados con modelos de recuperación de parámetros a partir del primer y del segundo momento de la distribución (diámetro medio y varianza, respectivamente). Los resultados indicaron que ambos métodos fueron satisfactorios para predecir las distribuciones de frecuencias de diámetros. El método de recuperación de parámetros fue más preciso que el método de predicción de parámetros

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

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

Ecos de la academia: Revista de la Facultad de Educación, Ciencia y Tecnología - FECYT Nro 6

Ecos de la academia, Revista de la Facultad de Educación Ciencia y Tecnología es una publicación científica de la Universidad Técnica del Norte, con revisión por pares a doble ciego que publica artículos en idioma español, quichua, portugués e inglés. Se edita con una frecuencia semestral con dos números por año.En ella se divulgan trabajos originales e inéditos generados por los investigadores, docentes y estudiantes de la FECYT, y contribuciones de profesionales de instituciones docentes e investigativas dentro y fuera del país, con calidad, originalidad y relevancia en las áreas de ciencias sociales y tecnología aplicada.Modelos multidimensionales del bienestar en contextos de enseñanza- aprendizaje: una revisión sistemática. Nuevas tendencias para el área académica de la Publicidad en la zona 1 del Ecuador. Propuesta de un curso de escritura académica bajo la base de modelos experienciales. Aproximación al estudio de las emociones. Seguimiento a egresados y graduados para actualizar el perfil de egreso y profesional. Impacto de la Gerencia de Calidad en el clima organizacional en Educación Básica. Comunicación efectiva del gerente educativo orientada al manejo de conflictos en el personal docente. Meritocracia: Democratización o exclusión en el acceso a la educación superior en Ecuador. Asertividad y desempeño académico en estudiantes universitarios. La creatividad en la formación profesional. Aspectos metodológicos en el proceso de enseñanza- aprendizaje de la gimnasia en estudiantes de Educación Física. English Language Learning Interaction through Web 2.0 Technologies. La sistematización de la práctica educativa y su relación con la metodología de la investigación. El ozono y la oxigenación hiperbárica: una vía para mejorar la recuperación en lesiones deportivas. La labor tutorial: Independencia del aprendizaje en el contexto universitario. Motivación hacia la profesión docente en la Enseñanza Secundaria. El uso académico de Facebook y WhatsApp en estudiantes universitarios... La educación superior en Ecuador: situación actual y factores de mejora de la calidad. El Proyecto de Investigación “Imbabura Étnica”

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 cases

Use of Gumbel and Weibull functions to model extreme values of diameter distributions in forest stands

International audience& Context Families of the Gumbel (type I), Fréchet (type II) and Weibull (type III) distributions can be combined in the generalized extreme value (GEV) family of distributions. Maximum and minimum values of diameters in forest stands can be used in forest modelling, mainly to define parameters of the functions used in diameter class models as well as in some practical cases, such as modelling maximum diameters for sawing and processing purposes. & Aims The purpose of this study was to examine and compare two extreme value distribution functions (the Gumbel and the Weibull functions) in modelling the distribution of the mini-mum and the maximum values of representative sets of tree diameter samples. Both of these functions were applied to the lower and upper values of the diameter distributions of the main forest species in northwest Spain: Quercus robur L., Betula pubescens Ehrh., Pinus radiata D. Don, Pinus pinaster Ait. and Pinus sylvestris L. & Methods Parameters of the Gumbel function were estimated using the mode and the moments of the distributions, and parameters of the Weibull function were estimated using the moments method. & Results In general, the Weibull distribution was the most suitable model for describing the maximum diameters. The mode method of the Gumbel yielded the best results for minimum diameters of birch and Monterrey pine. The Gumbel distribution, fitted by either the mode-or moments-based methods, proved more suitable than the Weibull distri-bution for describing the minimum diameters in maritime pine and Scots pine stands. & Conclusion In some cases, better results were obtained with the Gumbel than the Weibull distribution for de-scribing the distribution of extreme diameter values in forest stands in northwest Spain. This is the first exam-ple of the application of the Gumbel distribution in forest modelling

Crecimiento y tablas de producción de Pinus radiata D. Don en Galicia

In this paper, growth models and yield tables for Pinus radiata D. in Galicia (northwest of Spain) are shown. These models were obtained from the measurement of 175 permanent sample plots, stem analyses of dominant trees and index trees. Polymorphic site index curves and three different types of yield tables corresponding to other three possible stand density evolutions are obtained. Optimal biomass rotations range from 28 to 44 years, and mean annual increment varies from 8.1 to 19.8 m3 ha–1year–1 at 30 years, depending on site index. Wood productions to different standard diameters are estimated, and alternative silvicultural regimes are discussed.En este trabajo se exponen modelos de crecimiento y producción de Pinus radiata D. Don en Galicia a partir de una sola medición de parcelas de inventario, y del análisis de troncos de árboles dominantes y árboles tipo. Se obtiene un modelo de curvas de calidad de estación polimórfico y tres tipos diferentes de tablas de producción para otras tantas posibles evoluciones de la densidad de las parcelas. El turno de máxima renta en especie varía entre 28 y 44 años, y el crecimiento medio de la masa principal a los 30 años entre 8,1 y 19,8 m3/ha•año. Se estima la producción maderable según el volumen a diferentes valores estándar del diámetro final con corteza y se comparan las alternativas desde un punto de vista productivo