Search results
Results from the WOW.Com Content Network
Total variation distance is half the absolute area between the two curves: Half the shaded area above. In probability theory , the total variation distance is a distance measure for probability distributions.
The accuracy ratio (AR) is defined as the ratio of the area between the model CAP and random CAP, and the area between the perfect CAP and random CAP. [2] In a successful model, the AR has values between zero and one, and the higher the value is, the stronger the model. The cumulative number of positive outcomes indicates a model's strength.
Confidence bands can be constructed around estimates of the empirical distribution function.Simple theory allows the construction of point-wise confidence intervals, but it is also possible to construct a simultaneous confidence band for the cumulative distribution function as a whole by inverting the Kolmogorov-Smirnov test, or by using non-parametric likelihood methods.
In a graphical representation of the continuous uniform distribution function [()], the area under the curve within the specified bounds, displaying the probability, is a rectangle. For the specific example above, the base would be 16 , {\displaystyle 16,} and the height would be 1 23 . {\displaystyle {\tfrac {1}{23}}.} [ 5 ]
Figure 1: The left graph shows a probability density function. The right graph shows the cumulative distribution function. The value at a in the cumulative distribution equals the area under the probability density curve up to the point a. Absolutely continuous probability distributions can be described in several ways.
The peak is "well-sampled", so that less than 10% of the area or volume under the peak (area if a 1D Gaussian, volume if a 2D Gaussian) lies outside the measurement region. The width of the peak is much larger than the distance between sample locations (i.e. the detector pixels must be at least 5 times smaller than the Gaussian FWHM).
This probability is given by the integral of this variable's PDF over that range—that is, it is given by the area under the density function but above the horizontal axis and between the lowest and greatest values of the range. The probability density function is nonnegative everywhere, and the area under the entire curve is equal to 1.
The main criticism to the ROC curve described in these studies regards the incorporation of areas with low sensitivity and low specificity (both lower than 0.5) for the calculation of the total area under the curve (AUC)., [19] as described in the plot on the right.