Some observations on fitting assumed diameter distributions to horizontal point sampling data

2000 ◽  
Vol 30 (4) ◽  
pp. 521-533 ◽  
Author(s):  
Jeffrey H Gove
Keyword(s):  
Diameter Distribution ◽  
Parameter Estimates ◽  
Sample Point ◽  
Underlying Distribution ◽  
Weighted Distribution ◽  
Reliable Parameter ◽  
Simulation Results ◽  
Larger Sample ◽  
Horizontal Point Sampling ◽  
Diameter Distributions

This paper revisits the link between assumed diameter distributions arising from horizontal point samples and their unbiased stand-based representation through weighted distribution theory. Examples are presented, which show that the assumption of a common shared parameter set between these two distributional forms, while theoretically valid, may not be reasonable in many operational cases. Simulation results are presented, which relate the conformity (or lack thereof) in these estimates to sampling intensity per point and the underlying shape of the population diameter distribution from which the sample point was drawn. In general, larger sample sizes per point are required to yield reliable parameter estimates than are generally taken for inventory purposes. In addition, a complimentary finding suggests that the more positively skewed the underlying distribution, the more trees per point are required for good parameter estimates.

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.

Human respiratory input impedance from 4 to 200 Hz: physiological and modeling considerations

1988 ◽  
Vol 64 (2) ◽  
pp. 823-831 ◽  
Author(s):  
H. L. Dorkin ◽  
K. R. Lutchen ◽  
A. C. Jackson
Keyword(s):  
Input Impedance ◽  
Element Model ◽  
Forced Oscillations ◽  
Parameter Estimates ◽  
Tissue Resistance ◽  
Thoracic Gas Volume ◽  
Reliable Parameter ◽  
Quarter Wave ◽  
Lumped Element Model ◽  
Gas Volume

Recent studies on respiratory impedance (Zrs) have predicted that at frequencies greater than 64 Hz a second resonance will occur. Furthermore, if one intends to fit a model more complicated than the simple series combination of a resistance, inertance, and compliance to Zrs data, the only way to ensure statistically reliable parameter estimates is to include data surrounding this second resonance. An additional question, however, is whether the resulting parameters are physiologically meaningful. We obtained input impedance data from eight healthy adult humans using discrete frequency forced oscillations from 4 to 200 Hz. Three resonant frequencies were seen: 8 +/- 2, 151 +/- 10, and 182 +/- 16 Hz. A seven-parameter lumped element model provided an excellent fit to the data in all subjects. This model consists of an airway resistance (Raw), which is linearly dependent on frequency, and airway inertance separated from a tissue resistance, inertance, and compliance by a shunt compliance (Cg) thought to represent gas compressibility. Model estimates of Raw and Cg were compared with those suggested by measurement of Raw and thoracic gas volume using a plethysmograph. In all subjects the model Raw and Cg were significantly lower than and not correlated with the corresponding plethysmographic measurement. We hypothesize that the statistically reliable but physiologically inconsistent parameters are a consequence of the distorting influence of airway wall compliance and/or airway quarter-wave resonance. Such factors are not inherent to the seven-parameter model.

Selective Synthesis of Single-Walled Carbon Nanotubes by Blending Catalysts

2007 ◽  
Author(s):  
Shuhei Inoue ◽  
Takeshi Nakajima ◽  
Kazuya Nomura ◽  
Yoshihiro Kikuchi
Keyword(s):  
Carbon Nanotubes ◽  
Fermi Level ◽  
Chemical Vapor ◽  
Single Walled Carbon Nanotubes ◽  
Diameter Distribution ◽  
Efficient Catalyst ◽  
Single Walled Carbon ◽  
Similar Density ◽  
Walled Carbon Nanotubes ◽  
Diameter Distributions

Single-walled carbon nanotubes are considered the most attractive material and a lot of synthesis processes are developed. Among these synthesis processes chemical vapor deposition processes are considered to be most suitable for macroscopic production. In many CVD processes the alcohol catalytic CVD process can be the best process because it can produce very pure nanotubes without any purification. However, cobalt is essential as a catalyst that makes the flexibility of catalysts restricted. In this paper, our investigation mainly focused on as follows: The efficiency of combined catalysts with/without cobalt. The diameter distributions against catalysts density. The electrical states of catalysts near Fermi level. Consequently, almost all of cobalt containing catalysts worked well, and the diameter distributions were proportional to the particle size. Efficient catalysts had enough states around Fermi level and the cobalt-less efficient catalyst cluster model showed the similar density of state to the cobalt cluster. Thus, noticing to the DOS, other efficient catalysts can be discovered and the diameter distribution will be controllable by adjusting temperature, a catalyst size, and a catalyst combination without any complicated techniques and facilities.

scholarly journals MGMM: An R Package for fitting Gaussian Mixture Models on Incomplete Data

2019 ◽  
Author(s):  
Zachary R. McCaw ◽  
Hanna Julienne ◽  
Hugues Aschard
Keyword(s):  
Missing Data ◽  
Mixture Models ◽  
Gaussian Mixture Models ◽  
Model Fitting ◽  
Simulated Data ◽  
R Package ◽  
Gaussian Mixture ◽  
Parameter Estimates ◽  
Cluster Assignment ◽  
Underlying Distribution

AbstractAlthough missing data are prevalent in applications, existing implementations of Gaussian mixture models (GMMs) require complete data. Standard practice is to perform complete case analysis or imputation prior to model fitting. Both approaches have serious drawbacks, potentially resulting in biased and unstable parameter estimates. Here we present MGMM, an R package for fitting GMMs in the presence of missing data. Using three case studies on real and simulated data sets, we demonstrate that, when the underlying distribution is near-to a GMM, MGMM is more effective at recovering the true cluster assignments than state of the art imputation followed by standard GMM. Moreover, MGMM provides an accurate assessment of cluster assignment uncertainty even when the generative distribution is not a GMM. This assessment may be used to identify unassignable observations. MGMM is available as an R package on CRAN: https://CRAN.R-project.org/package=MGMM.

scholarly journals Comparing the State-of-the-Art Efficient Stated Choice Designs Based on Empirical Analysis

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Li Tang ◽  
Xia Luo ◽  
Yang Cheng ◽  
Fei Yang ◽  
Bin Ran
Keyword(s):  
Discrete Choice ◽  
State Of The Art ◽  
Choice Model ◽  
Orthogonal Design ◽  
Asymptotic Variance ◽  
Parameter Estimates ◽  
Efficient Design ◽  
Stated Choice ◽  
Reliable Parameter ◽  
Efficient Data

The stated choice (SC) experiment has been generally regarded as an effective method for behavior analysis. Among all the SC experimental design methods, the orthogonal design has been most widely used since it is easy to understand and construct. However, in recent years, a stream of research has put emphasis on the so-called efficient experimental designs rather than keeping the orthogonality of the experiment, as the former is capable of producing more efficient data in the sense that more reliable parameter estimates can be achieved with an equal or lower sample size. This paper provides two state-of-the-art methods called optimal orthogonal choice (OOC) andD-efficient design. More statistically efficient data is expected to be obtained by either maximizing attribute level differences, or minimizing theD-error, a statistic corresponding to the asymptotic variance-covariance (AVC) matrix of the discrete choice model, when using these two methods, respectively. Since comparison and validation in the field of these methods are rarely seen, an empirical study is presented.D-error is chosen as the measure of efficiency. The result shows that both OOC andD-efficient design are more efficient. At last, strength and weakness of orthogonal, OOC, andD-efficient design are summarized.

Some Results on the Behavior of Alternate Covariance Structure Estimation Procedures in the Presence of Non-Normal Data

1989 ◽  
Vol 26 (2) ◽  
pp. 214-221 ◽  
Author(s):  
Subhash Sharma ◽  
Srinivas Durvasula ◽  
William R. Dillon
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Covariance Structure ◽  
Standard Errors ◽  
Parameter Estimates ◽  
Simulation Experiments ◽  
Estimation Techniques ◽  
Structure Estimation ◽  
Estimation Procedures ◽  
Simulation Results

The authors report some results on the behavior of alternative covariance structure estimation procedures in the presence of non-normal data. They conducted Monté Carlo simulation experiments with a factorial design involving three levels of skewness, three level of kurtosis, and three different sample sizes. For normal data, among all the elliptical estimation techniques, elliptical reweighted least squares (ERLS) was equivalent in performance to ML. However, as expected, for non-normal data parameter estimates were unbiased for ML and the elliptical estimation techniques, whereas the bias in standard errors was substantial for GLS and ML. Among elliptical estimation techniques, ERLS was superior in performance. On the basis of the simulation results, the authors recommend that researchers use ERLS for both normal and non-normal data.

Adaptive Mismatch Compensation for Rate Integrating Vibratory Gyroscopes With Improved Convergence Rate

2014 ◽  
Author(s):  
Fu Zhang ◽  
Ehsan Keikha ◽  
Behrooz Shahsavari ◽  
Roberto Horowitz
Keyword(s):  
Convergence Rate ◽  
Degrees Of Freedom ◽  
Rotation Angle ◽  
Least Square ◽  
Parameter Estimates ◽  
Unknown Parameters ◽  
Least Square Estimator ◽  
Vibratory Gyroscopes ◽  
Adaptive Compensator ◽  
Simulation Results

This paper presents an online adaptive algorithm to compensate damping and stiffness frequency mismatches in rate integrating Coriolis Vibratory Gyroscopes (CVGs). The proposed adaptive compensator consists of a least square estimator that estimates the damping and frequency mismatches, and an online compensator that corrects the mismatches. In order to improve the adaptive compensator’s convergence rate, we introduce a calibration phase where we identify relations between the unknown parameters (i.e. mismatches, rotation rate and rotation angle). Calibration results show that the unknown parameters lie on a hyperplane. When the gyro is in operation, we project parameters estimated from the least square estimator onto the hyperplane. The projection will reduce the degrees of freedom in parameter estimates, thus guaranteeing persistence of excitation and improving convergence rate. Simulation results show that utilization of the projection method will drastically improve convergence rate of the least square estimator and improve gyro performance.

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.

scholarly journals Robust calibration of hierarchical population models for heterogeneous cell populations

2019 ◽  
Author(s):  
Carolin Loos ◽  
Jan Hasenauer
Keyword(s):  
Simulation Study ◽  
Population Model ◽  
Model Calibration ◽  
Cellular Heterogeneity ◽  
Parameter Estimates ◽  
List Type ◽  
Real World Application ◽  
Cellular Decision Making ◽  
Reliable Parameter ◽  
Distribution Assumption

AbstractCellular heterogeneity is known to have important effects on signal processing and cellular decision making. To understand these processes, multiple classes of mathematical models have been introduced. The hierarchical population model builds a novel class which allows for the mechanistic description of heterogeneity and explicitly takes into account subpopulation structures. However, this model requires a parametric distribution assumption for the cell population and, so far, only the normal distribution has been employed. Here, we incorporate alternative distribution assumptions into the model, assess their robustness against outliers and evaluate their influence on the performance of model calibration in a simulation study and a real-world application example. We found that alternative distributions provide reliable parameter estimates even in the presence of outliers, and can in fact increase the convergence of model calibration.HighlightsGeneralizes hierarchical population model to various distribution assumptionsProvides framework for efficient calibration of the hierarchical population modelSimulation study and application to experimental data reveal improved robustness and optimization performance

Sign in / Sign up

Export Citation Format

Share Document