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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 distance measure for probability distributions.
The total variation distance of two distributions and over a finite domain , (often referred to as statistical difference [2] or statistical distance [3] in ...
In probability and statistics, the Hellinger distance (closely related to, although different from, the Bhattacharyya distance) is used to quantify the similarity between two probability distributions. It is a type of f-divergence. The Hellinger distance is defined in terms of the Hellinger integral, which was introduced by Ernst Hellinger in 1909.
Notably, except for total variation distance, all others are special cases of -divergence, or linear sums of -divergences. For each f-divergence D f {\displaystyle D_{f}} , its generating function is not uniquely defined, but only up to c ⋅ ( t − 1 ) {\displaystyle c\cdot (t-1)} , where c {\displaystyle c} is any real constant.
The Jensen–Shannon divergence is bounded by 1 for two probability distributions, given that one uses the base 2 logarithm: [8] ().With this normalization, it is a lower bound on the total variation distance between P and Q:
In mathematics, the total variation identifies several slightly different concepts, related to the (local or global) structure of the codomain of a function or a measure.For a real-valued continuous function f, defined on an interval [a, b] ⊂ R, its total variation on the interval of definition is a measure of the one-dimensional arclength of the curve with parametric equation x ↦ f(x ...
The "70.3" refers to the total distance in miles (113.0 km) covered in the race, consisting of a 1.2-mile (1.9 km) swim, a 56-mile (90 km) bike ride, and a 13.1-mile (21.1 km) run. Each distance of the swim, bike, and run segments is half the distance of that segment in an Ironman Triathlon. The Ironman 70.3 series culminates each year with a ...
Distance, the total distance an object travels dependent on its path through space; Optical path length, the product of the distance light travels and the refractive index of the medium it travels through; Mean free path, the average distance that a particle travels before scattering