scholarly journals A percentile-based estimator for the log-logistic function: Application to forestry

2020 ◽  
Vol 72 (1) ◽  
pp. 107-120
Author(s):  
Friday Nwabueze Ogana
Keyword(s):  
Estimation Method ◽  
Tectona Grandis ◽  
Logistic Function ◽  
Growth And Yield ◽  
Estimation Methods ◽  
Diameter Distribution ◽  
Logistic Distribution ◽  
Forest Stands ◽  
Forest Modelling ◽  
Diameter Distributions

AbstractDeveloping a simplified estimation method without compromising the performance of the distribution is germane to forest modelling. Few estimation methods exist for the Log-Logistic distribution and are relatively complex. A simplified estimator for the Log-Logistic parameters will increase its application in diameter distribution yield systems. Therefore, in this study, a percentile-based estimator was applied for the Log-Logistic distribution. The Kolmogorov-Smirnov, Anderson-Darling and Cramer-von Mises statistics were used to evaluate the method in two natural forest stands and two monospecific plantations of Gmelina arborea Roxb. and Tectona grandis Linn. f. in Nigeria. The parameter recovery model (PRM) and parameter prediction model (PPM) were used to predict the diameter distributions of independent stands of G. arborea and T. grandis. The results showed that the percentile estimator did not compromise the quality of fits of the Log-Logistic function across the four forest stands and are comparable to the maximum likelihood estimator. The 25th and 75th, and 40th and 80th were the best sample percentiles for the estimator. The predicted diameter distributions of G. arborea and T. grandis stands from the PRM and PPM were reasonable and compare well with the observed distribution. Thus, either of the models can be incorporated into the growth and yield system of forest stand management.

scholarly journals Diameter distribution model development of tropical hybrid Eucalyptus clonal plantations in Sumatera, Indonesia: A comparison of estimation methods

2022 ◽  
Vol 52 ◽  
Author(s):  
Joni Waldy ◽  
John A. Kershaw Jr ◽  
Aaron Weiskittel ◽  
Mark J. Ducey
Keyword(s):  
Growth And Yield ◽  
Estimation Methods ◽  
Hybrid Clone ◽  
Distribution Model ◽  
Diameter Distribution ◽  
Average Growth ◽  
Eucalyptus Hybrid ◽  
Stand Attributes ◽  
The Moment ◽  
Diameter Distributions

Background: Effective forest management and planning often requires information about the distribution of volume by size and product classes. Size-class models describe the diameter distribution and provide information by diameter class, such as the number of trees, basal area, and volume per unit of area. A successful diameter-distribution model requires high flexibility yet robust prediction of its parameters. To our knowledge, there are no studies regarding diameter distribution models for Eucalyptus hybrids in Indonesia. Therefore, the aim of this study was to compare different recovery methods for predicting parameters of the 3-parameter Weibull distribution for characterising diameter distributions of Eucalyptus hybrid clone plantations, on Sumatera Island of Indonesia. Methods: The parameter recovery approach was proposed to be compatible with stand-average growth and yield models developed based on the same data. Three approaches where compared: moment-based recovery, percentile-based prediction and hybrid methods. The ultimate goal was to recover Weibull parameters from future stand attributes, which were predicted from current stand attributes using regression models. Results: In this study, the moment method was found to give the overall lowest mean error-index and Kolmogorov– Smirnov (KS) statistic, followed by the hybrid and percentile methods. The moment-based method better fit long tails on both sides of the distribution and exhibited slightly greater flexibility in describing plots with larger variance than the other methods. Conclusions: The Weibull approach appeared relatively robust in determining diameter distributions of Eucalyptus hybrid clone plantation in Indonesia, yet some refinements may be necessary to characterize more complex distributions.

A Blind Spot in the Use of the Weibull Function for Modeling Diameter Distributions

2020 ◽  
Author(s):  
Adrian Norman Goodwin
Keyword(s):  
Lower Bound ◽  
Blind Spot ◽  
Forest Growth ◽  
Growth And Yield ◽  
Diameter Distribution ◽  
Absolute Difference ◽  
Weibull Function ◽  
Distribution Models ◽  
Difference Statistic ◽  
Diameter Distributions

Abstract Diameter distribution models based on probability density functions are integral to many forest growth and yield systems, where they are used to estimate product volumes within diameter classes. The three-parameter Weibull function with a constrained nonnegative lower bound is commonly used because of its flexibility and ease of fitting. This study compared Weibull and reverse Weibull functions with and without a lower bound constraint and left-hand truncation, across three large unthinned plantation cohorts in which 81% of plots had negatively skewed diameter distributions. Near-optimal lower bounds for the unconstrained Weibull function were negative for negatively skewed data, and the left-truncated Weibull using these bounds was 14.2% more accurate than the constrained Weibull, based on the Kolmogorov-Smirnov statistic. The truncated reverse Weibull fit dominant tree distributions 23.7% more accurately than the constrained Weibull, based on a mean absolute difference statistic. This work indicates that a blind spot may have developed in plantation growth modeling systems deploying constrained Weibull functions, and that left-truncation of unconstrained functions could substantially improve model accuracy for negatively skewed distributions.

Deriving Tree Diameter Growth and Probability of Survival Equations from Successive Diameter Distributions

2008 ◽  
Vol 54 (1) ◽  
pp. 31-35
Author(s):  
Thomas G. Matney ◽  
Emily B. Schultz
Keyword(s):  
General Procedure ◽  
Growth And Yield ◽  
Diameter Distribution ◽  
Diameter Growth ◽  
Individual Tree ◽  
Statistical Probability ◽  
Growth And Survival ◽  
Tree Diameter ◽  
Growth And Yield Models ◽  
Diameter Distributions

Abstract Many growth and yield models have used statistical probability distributions to estimate the diameter distribution of a stand at any age. Equations for approximating individual tree diameter growth and survival probabilities from dbh can be derived from these models. A general procedure for determining the functions is discussed and illustrated using a loblolly pine spacing study. The results from the spacing study show that it is possible to define tree diameter growth and survival probability functions from diameter distributions with an accuracy sufficient to obtain a link between the individual tree and diameter growth and yield models.

A finite mixture of two Weibull distributions for modeling the diameter distributions of rotated-sigmoid, uneven-aged stands

2001 ◽  
Vol 31 (9) ◽  
pp. 1654-1659 ◽  
Author(s):  
Lianjun Zhang ◽  
Jeffrey H Gove ◽  
Chuangmin Liu ◽  
William B Leak
Keyword(s):  
Model Fitting ◽  
Mixture Distribution ◽  
Finite Mixture ◽  
Diameter Distribution ◽  
Weibull Distributions ◽  
Forest Stands ◽  
Negative Exponential Function ◽  
Diameter Frequency Distribution ◽  
Negative Exponential ◽  
Diameter Distributions

The rotated-sigmoid form is a characteristic of old-growth, uneven-aged forest stands caused by past disturbances such as cutting, fire, disease, and insect attacks. The diameter frequency distribution of the rotated-sigmoid form is bimodal with the second rounded peak in the midsized classes, rather than a smooth, steeply descending, monotonic curve. In this study a finite mixture of two Weibull distributions is used to describe the diameter distributions of the rotated-sigmoid, uneven-aged forest stands. Four example stands are selected to demonstrate model fitting and comparison. Compared with a single Weibull or negative exponential function, the finite finite mixture model is the only one that fits the diameter distributions well and produces root mean square error at least four times smaller than the other two. The results show that the finite mixture distribution is a better alternative method for modeling the diameter distribution of the rotated-sigmoid, uneven-aged forest stands.

Calibrating predicted diameter distribution with additional information in growth and yield predictions

2003 ◽  
Vol 33 (3) ◽  
pp. 430-434 ◽  
Author(s):  
Annika Kangas ◽  
Matti Maltamo
Keyword(s):  
Growth Models ◽  
Basal Area ◽  
Growth And Yield ◽  
Diameter Distribution ◽  
Individual Tree ◽  
Forest Management Planning ◽  
Growing Stock ◽  
Additional Information ◽  
Tree Models ◽  
Diameter Distributions

Diameter distribution of the growing stock is essential in many forest management planning problems. The diameter distribution is the basis for predicting, for example, timber assortments of a stand. Usually the predicted diameter distribution is scaled so that the stem number (or basal area) corresponds to the measured value (or predicted future value), but it may be difficult to obtain a distribution that gives correct estimates for all known variables. Diameter distributions that are compatible with all available information can be obtained using an approach adopted from sampling theory, the calibration estimation. In calibration estimation, the original predicted frequencies are modified so that they respect a set of constraints, the calibration equations. In this paper, an example of utilizing diameter distributions in growth and yield predictions is presented. The example is based on individual tree growth models of Scots pine (Pinus sylvestris L.). Calibration estimation was utilized in predicting the diameter distribution at the beginning of the simulation period. Then, trees were picked from the distribution and their development was predicted with individual tree models. In predicting the current stand characteristics, calibrated diameter distributions proved to be efficient. However, in predicting future yields, calibration estimation did not significantly improve the accuracy of the results.

Tree diameter distribution modelling: introducing the logit–logistic distribution

2005 ◽  
Vol 35 (6) ◽  
pp. 1305-1313 ◽  
Author(s):  
Mingliang Wang ◽  
Keith Rennolls
Keyword(s):  
Normal Distribution ◽  
Weibull Model ◽  
Diameter Distribution ◽  
Logistic Distribution ◽  
Parameter Distribution ◽  
Forest Modelling ◽  
Logit Transformation ◽  
Distribution Shape ◽  
Tree Diameter Distribution

Johnson's SB distribution is a four-parameter distribution that is transformed into a normal distribution by a logit transformation. By replacing the normal distribution of Johnson's SB with the logistic distribution, we obtain a new distributional model that approximates SB. It is analytically tractable, and we name it the "logit–logistic" (LL) distribution. A generalized four-parameter Weibull model and the Burr XII model are also introduced for comparison purposes. Using the distribution "shape plane" (with axes skew2 and kurtosis) we compare the "coverage" properties of the LL, the generalized Weibull, and the Burr XII with Johnson's SB, the beta, and the three-parameter Weibull, the main distributions used in forest modelling. The LL is found to have the largest range of shapes. An empirical case study of the distributional models is conducted on 107 sample plots of Chinese fir. The LL performs best among the four-parameter models.

A comparison of estimation methods for fitting Weibull and Johnson's SB distributions to mixed spruce–fir stands in northeastern North America

2003 ◽  
Vol 33 (7) ◽  
pp. 1340-1347 ◽  
Author(s):  
Lianjun Zhang ◽  
Kevin C Packard ◽  
Chuangmin Liu
Keyword(s):  
Maximum Likelihood ◽  
North America ◽  
Forest Type ◽  
Estimation Method ◽  
Abies Balsamea ◽  
Likelihood Estimation ◽  
Estimation Methods ◽  
Frequency Distributions ◽  
Northeastern North America ◽  
Diameter Distributions

Four commonly used estimation methods were employed to fit the three-parameter Weibull and Johnson's SB distributions to the tree diameter distributions of natural pure and mixed red spruce (Picea rubens Sarg.) – balsam fir (Abies balsamea (L.) Mill.) stands, respectively, in northeastern North America. The results indicated that the Weibull and the Johnson's SB distributions were, in general, equally suitable for modeling the diameter frequency distributions of this forest type, but the relative performance directly depended on the estimation method used. In this study, the linear regression methods for Johnson's SB were found to give the lowest mean Reynolds' error indices. The conditional maximum likelihood for Johnson's SB and the maximum likelihood estimation for Weibull produced comparable results. However, moment- or mode-based methods were not well suited to the observed diameter distributions that were typically positively skewed, reverse-J, and mound shapes.

scholarly journals PILOT STUDY ON THE RETRIEVAL OF DBH AND DIAMETER DISTRIBUTION OF DECIDUOUS FOREST STANDS USING CAST SHADOWS IN UAV-BASED ORTHOMOSAICS

2018 ◽  
Vol IV-1 ◽  
pp. 93-99 ◽  
Author(s):  
T. Kattenborn ◽  
J. Hernández ◽  
J. Lopatin ◽  
G. Kattenborn ◽  
F. E. Fassnacht
Keyword(s):  
Pilot Study ◽  
Deciduous Forest ◽  
Basal Area ◽  
Aerial Imagery ◽  
Diameter Distribution ◽  
Forest Stands ◽  
Efficient Retrieval ◽  
Difficult Terrain ◽  
Diameter Distributions

<p><strong>Abstract.</strong> One fundamental metric to characterize trees and forest stands is the diameter at breast height (DBH). However, the vertical geometry of tree stems hampers a direct measurement by means of orthographic aerial imagery. Nevertheless, the DBH in deciduous forest stands could be measured from UAV-based imagery using the width of a stem´s cast shadow projected on the ground. Here, we compare in-situ measured DBH of 100 trees with the DBH visually interpreted from cast-shadows derived in UAV-based aerial imagery. Then, based on simulated datasets, we determine suitable DBH sampling sizes for a robust and efficient retrieval of stand diameter distributions. The UAV-based DBH estimation resulted in an r<sup>2</sup> of 0.74, RMSE of 7.61<span class="thinspace"></span>cm, NRMSE of 12.8<span class="thinspace"></span>% and approximately unbiased results. According to our simulations it can be assumed that a sample size of 25&amp;ndash;50 individual DBH measurements per forest stand allows estimating reliable diameter distributions. The presented pilot study gives a first insight on the potential of such an approach for operational assessments of diameter distribution in deciduous forest stands and might be particularly interesting for stands in difficult terrain situations. The presented approach can be extended to estimate the basal area, timber stock or biomass.</p>

Using The Fully Modified M Method In Estimating The Effect Of Cultivated Area On Barley Production In Iraq For The Period 1970-2018

2020 ◽  
Vol 2020 (66) ◽  
pp. 101-110
Author(s):  
. Azhar Kadhim Jbarah ◽  
Prof Dr. Ahmed Shaker Mohammed
Keyword(s):  
Regression Model ◽  
Moving Average ◽  
Estimation Method ◽  
Estimation Methods ◽  
Autoregressive Moving Average ◽  
Moving Average Models ◽  
Error Terms ◽  
Relationship Of ◽  
The Relationship ◽  
Barley Crop

The research is concerned with estimating the effect of the cultivated area of barley crop on the production of that crop by estimating the regression model representing the relationship of these two variables. The results of the tests indicated that the time series of the response variable values is stationary and the series of values of the explanatory variable were nonstationary and that they were integrated of order one ( I(1) ), these tests also indicate that the random error terms are auto correlated and can be modeled according to the mixed autoregressive-moving average models ARMA(p,q), for these results we cannot use the classical estimation method to estimate our regression model, therefore, a fully modified M method was adopted, which is a robust estimation methods, The estimated results indicate a positive significant relation between the production of barley crop and cultivated area.

scholarly journals Comparative Analysis of Kinect-Based and Oculus-Based Gaze Region Estimation Methods in a Driving Simulator

Sensors ◽  
2020 ◽  
Vol 21 (1) ◽  
pp. 26
Author(s):  
David González-Ortega ◽  
Francisco Javier Díaz-Pernas ◽  
Mario Martínez-Zarzuela ◽  
Míriam Antón-Rodríguez
Keyword(s):  
Virtual Reality ◽  
Comparative Analysis ◽  
Driving Simulator ◽  
Estimation Method ◽  
Estimation Methods ◽  
Gaze Estimation ◽  
Driving Simulators ◽  
Oculus Rift ◽  
Gaze Patterns ◽  
And Performance

Driver’s gaze information can be crucial in driving research because of its relation to driver attention. Particularly, the inclusion of gaze data in driving simulators broadens the scope of research studies as they can relate drivers’ gaze patterns to their features and performance. In this paper, we present two gaze region estimation modules integrated in a driving simulator. One uses the 3D Kinect device and another uses the virtual reality Oculus Rift device. The modules are able to detect the region, out of seven in which the driving scene was divided, where a driver is gazing at in every route processed frame. Four methods were implemented and compared for gaze estimation, which learn the relation between gaze displacement and head movement. Two are simpler and based on points that try to capture this relation and two are based on classifiers such as MLP and SVM. Experiments were carried out with 12 users that drove on the same scenario twice, each one with a different visualization display, first with a big screen and later with Oculus Rift. On the whole, Oculus Rift outperformed Kinect as the best hardware for gaze estimation. The Oculus-based gaze region estimation method with the highest performance achieved an accuracy of 97.94%. The information provided by the Oculus Rift module enriches the driving simulator data and makes it possible a multimodal driving performance analysis apart from the immersion and realism obtained with the virtual reality experience provided by Oculus.

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