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A distance between populations can be interpreted as measuring the distance between two probability distributions and hence they are essentially measures of distances between probability measures. Where statistical distance measures relate to the differences between random variables, these may have statistical dependence, [1] and hence these ...
In probability theory, the total variation distance is a distance measure for probability distributions. It is an example of a statistical distance metric, and is sometimes called the statistical distance, statistical difference or variational distance.
Its formal use dates at least to Bhattacharyya (1943), entitled "On a measure of divergence between two statistical populations defined by their probability distributions", which defined the Bhattacharyya distance, and Bhattacharyya (1946), entitled "On a Measure of Divergence between Two Multinomial Populations", which defined the ...
In statistics, the Bhattacharyya distance is a quantity which represents a notion of similarity between two probability distributions. [1] It is closely related to the Bhattacharyya coefficient , which is a measure of the amount of overlap between two statistical samples or populations.
In probability theory, integral probability metrics are types of distance functions between probability distributions, defined by how well a class of functions can distinguish the two distributions. Many important statistical distances are integral probability metrics, including the Wasserstein-1 distance and the total variation distance .
In mathematics, the Wasserstein distance or Kantorovich–Rubinstein metric is a distance function defined between probability distributions on a given metric space. It is named after Leonid Vaseršteĭn .
In mathematical statistics, the Kullback–Leibler (KL) divergence (also called relative entropy and I-divergence [1]), denoted (), is a type of statistical distance: a measure of how much a model probability distribution Q is different from a true probability distribution P.
In probability theory and statistics, the Jensen–Shannon divergence, named after Johan Jensen and Claude Shannon, is a method of measuring the similarity between two probability distributions. It is also known as information radius (IRad) [1] [2] or total divergence to the average. [3]
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