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In probability theory and statistics, the coefficient of variation (CV), also known as normalized root-mean-square deviation (NRMSD), percent RMS, and relative standard deviation (RSD), is a standardized measure of dispersion of a probability distribution or frequency distribution.
In probability theory and statistics, the index of dispersion, [1] dispersion index, coefficient of dispersion, relative variance, or variance-to-mean ratio (VMR), like the coefficient of variation, is a normalized measure of the dispersion of a probability distribution: it is a measure used to quantify whether a set of observed occurrences are clustered or dispersed compared to a standard ...
The Nash–Sutcliffe coefficient masks important behaviors that if re-cast can aid in the interpretation of the different sources of model behavior in terms of bias, random, and other components. [11]
In fluid dynamics, normalized root mean square deviation (NRMSD), coefficient of variation (CV), and percent RMS are used to quantify the uniformity of flow behavior such as velocity profile, temperature distribution, or gas species concentration. The value is compared to industry standards to optimize the design of flow and thermal equipment ...
The relative mean absolute difference quantifies the mean absolute difference in comparison to the size of the mean and is a dimensionless quantity. The relative mean absolute difference is equal to twice the Gini coefficient which is defined in terms of the Lorenz curve. This relationship gives complementary perspectives to both the relative ...
When a member of the exponential family has been specified, the variance function can easily be derived. [4]: 29 The general form of the variance function is presented under the exponential family context, as well as specific forms for Normal, Bernoulli, Poisson, and Gamma. In addition, we describe the applications and use of variance functions ...
It follows that the MSE of this function equals the variance of Y; that is, SS err = SS tot, and SS reg = 0. In this case, no variation in Y can be accounted for, and the FVU then has its maximum value of 1. More generally, the FVU will be 1 if the explanatory variables X tell us nothing about Y in the sense that the predicted values of Y do ...
For any index, the closer to uniform the distribution, the larger the variance, and the larger the differences in frequencies across categories, the smaller the variance. Indices of qualitative variation are then analogous to information entropy , which is minimized when all cases belong to a single category and maximized in a uniform distribution.