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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 statistical distance between probability distributions, and is sometimes called the statistical distance, statistical difference or variational distance.
A metric on a set X is a function (called the distance function or simply distance) d : X × X → R + (where R + is the set of non-negative real numbers). For all x, y, z in X, this function is required to satisfy the following conditions: d(x, y) ≥ 0 (non-negativity) d(x, y) = 0 if and only if x = y (identity of indiscernibles.
Gaussian curvature is the limiting difference between the circumference of a geodesic circle and a circle in the plane: [9] = + () Gaussian curvature is the limiting difference between the area of a geodesic disk and a disk in the plane: [ 9 ] K = lim r → 0 + 12 π r 2 − A ( r ) π r 4 {\displaystyle K=\lim _{r\to 0^{+}}12{\frac {\pi r^{2 ...
Repeat the following process until the difference between the computed ... 0.999999: 4.891 638 475 699: 0.99: 2.575 829 303 549: ... The area bounded by the curve and ...
The blue area above the x-axis may be specified as positive area, while the yellow area below the x-axis is the negative area. The integral of a real function can be imagined as the signed area between the x {\displaystyle x} -axis and the curve y = f ( x ) {\displaystyle y=f(x)} over an interval [ a , b ].
The area between two graphs can be evaluated by calculating the difference between the integrals of the two functions The area between a positive-valued curve and the horizontal axis, measured between two values a and b (b is defined as the larger of the two values) on the horizontal axis, is given by the integral from a to b of the function ...
In most studies, it has been found that the zROC curve slopes constantly fall below 1, usually between 0.5 and 0.9. [51] Many experiments yielded a zROC slope of 0.8. A slope of 0.8 implies that the variability of the target strength distribution is 25% larger than the variability of the lure strength distribution. [52]
The mean absolute difference (univariate) is a measure of statistical dispersion equal to the average absolute difference of two independent values drawn from a probability distribution. A related statistic is the relative mean absolute difference , which is the mean absolute difference divided by the arithmetic mean , and equal to twice the ...