Models for data with constant coefficient of variation

1989 ◽  
pp. 285-322 ◽  
Author(s):  
P. McCullagh ◽  
J. A. Nelder
Keyword(s):  
Coefficient Of Variation ◽  
Constant Coefficient ◽  
Constant Coefficient Of Variation

Understanding change in hydrometeorological extremes with statistical models - the importance of model parametrization

2021 ◽  
Author(s):  
Ilaria Prosdocimi ◽  
Thomas Kjeldsen
Keyword(s):  
Coefficient Of Variation ◽  
Constant Coefficient ◽  
River Flow ◽  
Extreme Value ◽  
Flow Measurements ◽  
Scaling Properties ◽  
Distribution Parameters ◽  
Quantile Estimates ◽  
Constant Coefficient Of Variation ◽  
The Impact

<p>The potential for changes in hydrometeorological extremes is routinely investigated by fitting change-permitting extreme value models to long-term observations, allowing one or more distribution parameters to change as a function of time or some physically-motivated covariate. In most practical extreme value analyses, the main quantity of interest though is the upper quantiles of the distribution, rather than the parameters' values. This study focuses on the changes in quantile estimates under different change-permitting models. First, metrics which measure the impact of changes in parameters on changes in quantiles are introduced. The mathematical structure of these change metrics is investigated for several models based on the Generalised Extreme Value (GEV) distribution. It is shown that for the most commonly used models, the predicted changes in the quantiles are a non-intuitive function of the distribution parameters, leading to results which are difficult to interpret. Next, it is posited that commonly used change-permitting GEV models do not preserve a constant coefficient of variation, a property that is typically assumed to hold and that is related to the scaling properties of extremes. To address these shortcomings a new (parsimonious) model is proposed: the model assumes a constant coefficient of variation, allowing the location and scale parameters to change simultaneously. The proposed model results in more interpretable changes in the quantile function. The consequences of the different modelling choices on quantile estimates are exemplified using a dataset of extreme peak river flow measurements.</p>

scholarly journals Analysis of algebraic weighted least-squares estimators for enzyme parameters

1992 ◽  
Vol 288 (2) ◽  
pp. 533-538 ◽  
Author(s):  
M E Jones
Keyword(s):  
Least Squares ◽  
Coefficient Of Variation ◽  
Constant Coefficient ◽  
Weighted Least Squares ◽  
Simulated Data ◽  
Standard Errors ◽  
Parameter Estimates ◽  
Spreadsheet Program ◽  
Least Squares Estimators ◽  
Constant Coefficient Of Variation

An algorithm for the least-squares estimation of enzyme parameters Km and Vmax. is proposed and its performance analysed. The problem is non-linear, but the algorithm is algebraic and does not require initial parameter estimates. On a spreadsheet program such as MINITAB, it may be coded in as few as ten instructions. The algorithm derives an intermediate estimate of Km and Vmax. appropriate to data with a constant coefficient of variation and then applies a single reweighting. Its performance using simulated data with a variety of error structures is compared with that of the classical reciprocal transforms and to both appropriately and inappropriately weighted direct least-squares estimators. Three approaches to estimating the standard errors of the parameter estimates are discussed, and one suitable for spreadsheet implementation is illustrated.

scholarly journals Parametrisation of change-permitting extreme value models and its impact on the description of change

2020 ◽  
Author(s):  
Ilaria Prosdocimi ◽  
Thomas Kjeldsen
Keyword(s):  
Coefficient Of Variation ◽  
Constant Coefficient ◽  
River Flow ◽  
Extreme Value ◽  
Flow Measurements ◽  
Environmental Extremes ◽  
Distribution Parameters ◽  
Quantile Estimates ◽  
Constant Coefficient Of Variation ◽  
The Impact

AbstractThe potential for changes in environmental extremes is routinely investigated by fitting change-permitting extreme value models to long-term observations, allowing one or more distribution parameters to change as a function of time or some other covariate. In most extreme value analyses, the main quantity of interest is typically the upper quantiles of the distribution, which are often needed for practical applications such as engineering design. This study focuses on the changes in quantile estimates under different change-permitting models. First, metrics which measure the impact of changes in parameters on changes in quantiles are introduced. The mathematical structure of these change metrics is investigated for several change-permitting models based on the Generalised Extreme Value (GEV) distribution. It is shown that for the most commonly used models, the predicted changes in the quantiles are a non-intuitive function of the distribution parameters, leading to results which are difficult to interpret. Next, it is posited that commonly used change-permitting GEV models do not preserve a constant coefficient of variation, a property that is typically assumed to hold for environmental extremes. To address these shortcomings a new (parsimonious) model is proposed: the model assumes a constant coefficient of variation, allowing the location and scale parameters to change simultaneously. The proposed model results in changes in the quantile function that are easier to interpret. Finally, the consequences of the different modelling choices on quantile estimates are exemplified using a dataset of extreme peak river flow measurements in Massachusetts, USA. It is argued that the decision on which model structure to adopt to describe change in extremes should also take into consideration any requirements on the behaviour of the quantiles of interest.

Mission: Impossible? Modelling the Verbal Estimation of Duration

2015 ◽  
Vol 3 (3-4) ◽  
pp. 223-245 ◽  
Author(s):  
J. H. Wearden
Keyword(s):  
Stimulus Duration ◽  
Coefficient Of Variation ◽  
Constant Coefficient ◽  
Final Value ◽  
Coefficients Of Variation ◽  
Verbal Estimation ◽  
Attractor Model ◽  
Competition Process ◽  
Scalar Properties ◽  
Constant Coefficient Of Variation

Three participants produced a large number of verbal estimates of tone durations in the range of 77–1183 ms. Data from this task were simulated by an ‘attractor model’, which used the idea of competition between ‘attractors’ (‘quantized’ values output as verbal estimates) which differed in weight, and distance from the stimulus duration to be estimated. To produce an estimate, all attractors competed for priority as output values, with the final value being decided probabilistically. The model embodied underlying scalar representations of time, in the form of mean accuracy and constant coefficient of variation. The model was able to reconcile such scalar properties of time with deviations from scalar properties often found in verbal estimation data, such as declining coefficients of variation with increasing duration value. The model furthermore showed that multiplicative and additive changes in underlying time representations should be translated veridically into behaviour, although the attractor competition process could distort patterns and absolute values of underlying variance.

scholarly journals Do estimates of numerosity really adhere to Weber’s law? A reexamination of two case studies

2020 ◽  
Author(s):  
Alberto Testolin ◽  
James L. McClelland
Keyword(s):  
Coefficient Of Variation ◽  
Constant Coefficient ◽  
Behavioral Data ◽  
Weber’S Law ◽  
Visual Array ◽  
Numerosity Discrimination ◽  
Weber's Law ◽  
The Mean ◽  
Numerosity Judgments ◽  
Constant Coefficient Of Variation

Abstract Both humans and nonhuman animals can exhibit sensitivity to the approximate number of items in a visual array or events in a sequence, and across various paradigms, uncertainty in numerosity judgments increases with the number estimated or produced. The pattern of increase is usually described as exhibiting approximate adherence to Weber’s law, such that uncertainty increases proportionally to the mean estimate, resulting in a constant coefficient of variation. Such a pattern has been proposed to be a signature characteristic of an innate “number sense.” We reexamine published behavioral data from two studies that have been cited as prototypical evidence of adherence to Weber’s law and observe that in both cases variability increases less than this account would predict, as indicated by a decreasing coefficient of variation with an increase in number. We also consider evidence from numerosity discrimination studies that show deviations from the constant coefficient of variation pattern. Though behavioral data can sometimes exhibit approximate adherence to Weber’s law, our findings suggest that such adherence is not a fixed characteristic of the mechanisms whereby humans and animals estimate numerosity. We suggest instead that the observed pattern of increase in variability with number depends on the circumstances of the task and stimuli, and reflects an adaptive ensemble of mechanisms composed to optimize performance under these circumstances.

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