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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 ...
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 sign of the covariance of two random variables X and Y. In probability theory and statistics, covariance is a measure of the joint variability of two random variables. [1] ...
The goal of experimental design is to construct experiments in such a way that when the observations are analyzed, the MSE is close to zero relative to the magnitude of at least one of the estimated treatment effects. In one-way analysis of variance, MSE can be calculated by the division of the sum of squared errors and the degree of freedom ...
Any non-linear differentiable function, (,), of two variables, and , can be expanded as + +. If we take the variance on both sides and use the formula [11] for the variance of a linear combination of variables (+) = + + (,), then we obtain | | + | | +, where is the standard deviation of the function , is the standard deviation of , is the standard deviation of and = is the ...
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 ...
Often, variation is quantified as variance; then, the more specific term explained variance can be used. The complementary part of the total variation is called unexplained or residual variation ; likewise, when discussing variance as such, this is referred to as unexplained or residual variance .