Predicting parameters of Weibull probability density function for diametric distributions in A. melanoxylon, E. camaldulensis, and E. nitens bioenergy plantation

Precise modeling of stand diameter distributions is required to provide accurate estimates of volume per diameter class and unit area. Therefore, it is necessary to obtain the most accurate probability density functions parameters estimates to predict stand diameter distribution in time. We evaluate two methods to estimate the parameters of the Weibull probability density function in the modeling of diameter distributions of bioenergy plantations. The methods considered a direct method of parameter prediction based on regression models (PPRM) and an indirect method of parameter recovery through the determination of percentiles (PRDP). Both methods are considered systems of linear equations and are adjusted through simultaneous estimation of parameters using stand variables. The greatest precision was obtained with PPRM. The PRDP method was not effective in the prediction of diameter distributions due to the high level of truncation of the observed distributions showing an overestimation of the distribution for the largest diameter classes. Estimated parameters of the Weibull PDF are directly related to mean height, quadratic mean diameter, and crop age; and are inversely related to stocking.

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Evaluation of three methods for predicting diameter distributions of black spruce (Picea mariana) plantations in central Canada

Canadian Journal of Forest Research ◽

10.1139/x04-117 ◽

2004 ◽

Vol 34 (12) ◽

pp. 2424-2432 ◽

Cited By ~ 21

Author(s):

Chuangmin Liu ◽

S Y Zhang ◽

Yuancai Lei ◽

Peter F Newton ◽

Lianjun Zhang

Keyword(s):

Probability Density Function ◽

Probability Density ◽

Density Function ◽

Picea Mariana ◽

Black Spruce ◽

Stand Age ◽

Recovery Method ◽

Parameter Recovery ◽

Central Canada ◽

Diameter Distributions

The direct parameter prediction method (PPM), moment-based parameter recovery method (PRM), and percentile-based parameter recovery method (PCT) for estimating the parameters of the three-parameter Weibull probability density function were evaluated for their applicability in predicting the diameter distribution of unthinned black spruce (Picea mariana (Mill.) B.S.P.) plantations. Employing diameter frequency data derived from 267 permanent sample plots situated throughout central Canada, fit (n = 214) and validation (n = 53) data sets were created. Using stepwise regression analyses in combination with seemingly unrelated regression techniques, the three methods were calibrated using commonly measured prediction variables (stand age, dominant height, site index, and stand density). Results indicated that, although all three methods were successful in predicting the diameter frequency distributions within the sample stands, the PCT was superior in terms of prediction error. Specifically, the PCT had the lowest mean error index (80.98), followed by the PRM (82.73) and the PPM (83.98). Consequently, among the three methods assessed, the PCT was considered the most suitable for describing unimodal diameter distributions via the three-parameter Weibull probability density function within unthinned black spruce plantations.

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Modelling the diameter distribution of eucalyptus plantations with Johnson’s S B probability density function: parameters recovery from a compatible system of equations to predict stand variables

Annals of Forest Science ◽

10.1007/s13595-011-0037-7 ◽

2011 ◽

Vol 68 (2) ◽

pp. 325-335 ◽

Cited By ~ 9

Author(s):

Ayana Mateus ◽

Margarida Tomé

Keyword(s):

Probability Density Function ◽

Probability Density ◽

Density Function ◽

Diameter Distribution ◽

System Of Equations ◽

Compatible System ◽

Eucalyptus Plantations

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Procedures for theoretical redistribution of diameters in eucalyptus stands

CERNE ◽

10.1590/s0104-77602010000100008 ◽

2010 ◽

Vol 16 (1) ◽

pp. 68-76 ◽

Cited By ~ 2

Author(s):

Thelma Shirlen Soares ◽

Hélio Garcia Leite ◽

Carlos Pedro Boechat Soares ◽

Antônio Bartolomeu do Vale

Keyword(s):

Probability Density Function ◽

Probability Density ◽

Density Function ◽

Eucalyptus Grandis ◽

Distribution Model ◽

Diameter Distribution ◽

Eucalyptus Urophylla ◽

Traditional Procedure ◽

Hybrid Eucalyptus ◽

Invariant Procedure

This study aimed to evaluate the application of a procedure referred to as step invariant for theoretical redistribution of diameters by class in a diameter distribution model, using the Weibull probability density function. Data from the first rotation of hybrid eucalyptus stands (Eucalyptus grandis x Eucalyptus urophylla) planted with spacings of 3 x 2 m, located in northeastern Bahia state were used. Measurements were taken annually with measurement age ranging between 25 and 89 months. The step invariant procedure provided satisfactory results in comparison to the traditional procedure, being therefore recommended for future applications due to its unbiased results and ease of fit.

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